Cun-quan Zhang - Academia.edu (original) (raw)
Papers by Cun-quan Zhang
For two positive integers k, r , a (k, r)-coloring (or r-hued k-coloring) of a graph G is a prope... more For two positive integers k, r , a (k, r)-coloring (or r-hued k-coloring) of a graph G is a proper k-vertex-coloring such that every vertex v of degree dG(v) is adjacent to at least min{dG(v), r} distinct colors. The r-hued chromatic number, χr (G), is the smallest integer k for which G has a (k, r)-coloring. The maximum average degree of G, denoted bymad (G), equals max{2|E(H)|/|V (H)|: H is a subgraph of G}. In this paper, we prove the following results using thewell-known dischargingmethod. For a graph G, if mad(G) < 12 5 , then χ3(G) ≤ 6; if mad(G) < 7 3 , then χ3(G) ≤ 5; if G has no C5-components and mad(G) < 3 , then χ2(G) ≤ 4. © 2017 Elsevier B.V. All rights reserved.
Discrete Mathematics, 2018
Jaeger, Linial, Payan and Tarsi (JCTB, 1992) introduced the concept of group connectivity as a ge... more Jaeger, Linial, Payan and Tarsi (JCTB, 1992) introduced the concept of group connectivity as a generalization of nowhere-zero flow for graphs. In this paper, we introduce group connectivity for signed graphs and establish some fundamental properties. For a finite abelian group A, it is proved that an A-connected signed graph is a contractible configuration for Aflow problem of signed graphs. In addition, we give sufficient edge connectivity conditions for signed graphs to be A-connected and study the group connectivity of some families of signed graphs.
International Journal of Pattern Recognition and Artificial Intelligence, 2016
Signed networks with both positive and negative links have gained considerable attention over the... more Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlapping communities, where a node is allowed to belong to multiple communities, widely exist in many real-world networks. Another disadvantage of some existing algorithms is that the number of final clusters k should be an input of the clustering process. It may however be the case that we do not know k in advance. In this paper, to offer improvements to existing algorithms, we propose a new clust...
Circuit Double Cover of Graphs
Circuit Double Cover of Graphs
Circuit Double Cover of Graphs
Discrete Applied Mathematics, 2018
Abstract For two positive integers k , r , a ( k , r ) -coloring (or r -hued k -coloring) of a gr... more Abstract For two positive integers k , r , a ( k , r ) -coloring (or r -hued k -coloring) of a graph G is a proper k -vertex-coloring such that every vertex v of degree d G ( v ) is adjacent to at least min { d G ( v ) , r } distinct colors. The r -hued chromatic number, χ r ( G ) , is the smallest integer k for which G has a ( k , r ) -coloring. The maximum average degree of G , denoted by mad ( G ) , equals max { 2 | E ( H ) | ∕ | V ( H ) | : H is a subgraph of G } . In this paper, we prove the following results using the well-known discharging method. For a graph G , if mad ( G ) 12 5 , then χ 3 ( G ) ≤ 6 ; if mad ( G ) 7 3 , then χ 3 ( G ) ≤ 5 ; if G has no C 5 -components and mad ( G ) 8 3 , then χ 2 ( G ) ≤ 4 .
The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published ... more The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published under the name QCM (quasi-clique merger) [12, 11, 24, 19]. The AQCM algorithm performs hierarchical clustering in any data set for which there is an associated similarity measure quantifying the similarity of any data i and data j. Importantly, the method exhibits two valuable performance properties: 1) the ability to automatically return either a larger or smaller number of clusters depending on the inherent properties of the data rather than on a parameter 2) the ability to return a very large number of relatively small clusters automatically when such clusters are reasonably well defined in a data set. In this work we present the general idea of a quasi-clique agglomerative approach, provide the full details of the mathematical steps of the AQCM algorithm, and explain some of the motivation behind the new methodology. The main achievement of the new methodology is that the agglomerati...
European Journal of Combinatorics, 2021
Abstract It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfe... more Abstract It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. This conjecture has been verified for many families of snarks with small ( ≤ 5 ) cyclic edge-connectivity. An infinite family, denoted by S K , of cyclically 6-edge-connected superposition snarks was constructed in [European J. Combin. 2002] by Kochol. In this paper, the Berge–Fulkerson conjecture is verified for the family S K , and, furthermore, some larger families containing S K . This is the first paper about the Berge–Fulkerson conjecture for superposition snarks and cyclically 6-edge-connected snarks. Tutte’s integer flow and Catlin’s contractible configuration are applied here as the key methods.
Circuit Double Cover of Graphs
Journal of Combinatorial Theory, Series B, 2020
In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-z... more In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero 6-flow. Bouchet himself proved that such signed graphs admit nowhere-zero 216-flows and Zýka further proved that such signed graphs admit nowherezero 30-flows. In this paper we show that every flow-admissible signed graph admits a nowhere-zero 11-flow.
Journal of Graph Theory, 2021
It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchi... more It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. Let G be a permutation graph with a 2‐factor F = { C 1 , C 2 } . A circuit C 0 is F ‐alternating if E ( C 0 ) ⧹ ( E ( C 1 ) ∪ E ( C 2 ) ) is a perfect matching of C 0 . A permutation graph G with a 2‐factor F = { C 1 , C 2 } is C ( 12 ) ‐linked if it contains an F ‐alternating circuit of length at most 12. It is proved in this paper that every C ( 12 ) ‐linked permutation graph is Berge–Fulkerson colorable. As an application, the conjecture is verified for some families of snarks constructed by Abreu et al., Brinkmann et al., and Hägglund et al.
Discrete Mathematics, Algorithms and Applications, 2020
The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertice... more The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. In this paper, we present a structural result on the graphs in [Formula: see text] with minimum Wiener index and completely characterize such graphs when [Formula: see text].
Journal of Graph Theory, 2018
A labeling of a digraph D with m arcs is a bijection from the set of arcs of D to {1,. .. , m}. A... more A labeling of a digraph D with m arcs is a bijection from the set of arcs of D to {1,. .. , m}. A labeling of D is antimagic if no two vertices in D have the same vertexsum, where the vertex-sum of a vertex u ∈ V (D) for a labeling is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Motivated by the conjecture of Hartsfield and Ringel from 1990 on antimagic labelings of graphs, Hefetz, Mütze, and Schwartz [On antimagic directed graphs, J Graph Theory 64 (2010) 219-232] initiated the study of antimagic labelings of digraphs, and conjectured that every connected graph admits an antimagic orientation, where an orientation D of a graph G is antimagic if D has an antimagic labeling. It remained unknown whether every disjoint union of cycles admits an antimagic orientation. In this paper, we first answer this question in the positive by proving that every 2-regular graph has an antimagic orientation. We then show that for any integer d ≥ 2, every connected, 2d-regular graph has an antimagic orientation. Our technique is new.
Journal of Graph Theory, 2017
It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchi... more It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. Let be a cubic graph and = { 1 , … , } be a 2-factor of such that | | is odd if and only if ≤ 2 for some integer. The 2factor is (8)-linked if, for every ≤ , there is a circuit of length 8 with edge sequence 1 … 8 where 1 , 5 ∈ (2 −1) and 3 , 7 ∈ (2). And the cubic graph is (8)-linked if it contains a (8)-linked 2-factor. It is proved in this article that every (8)-linked cubic graph is Berge-Fulkerson colorable. It is also noticed that many classical families of snarks (including some high oddness snarks) are (8)-linked. Consequently, the Berge-Fulkerson conjecture is verified for these infinite families of snarks.
Graphs and Combinatorics, 2015
Your article is protected by copyright and all rights are held exclusively by Springer Japan. Thi... more Your article is protected by copyright and all rights are held exclusively by Springer Japan. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
Circuit Double Cover of Graphs
Pattern Recognition Letters, 2011
In a graph theory model, clustering is the process of division of vertices into groups, with a hi... more In a graph theory model, clustering is the process of division of vertices into groups, with a higher density of edges within groups than between them. In this paper, we introduce a new clustering method for detecting such groups and use it to analyse some classic social networks. The new method has two distinguished features: non-binary hierarchical tree and the feature of overlapping clustering. A non-binary hierarchical tree is much smaller than the binary-trees constructed by most traditional methods and, therefore, it clearly highlights meaningful clusters which significantly reduces further manual efforts for cluster selections. The present method is tested by several bench mark data sets for which the community structure was known beforehand and the results indicate that it is a sensitive and accurate method for extracting community structure from social networks.
Journal of Information and Optimization Sciences, 1984
If a tournament T is said to satisfy O(p, q) condition, then d+(uHd-(v);;>p-q for each arc VII in... more If a tournament T is said to satisfy O(p, q) condition, then d+(uHd-(v);;>p-q for each arc VII in T, wha re p = I VeT) I , q is an integer. Let T be a tournament satis fying O{p,q) condition. Alspach [1] proved that T is arc-pancyclic when q= 1. Zhu and Tian [2] proved that T is arc-pancyclic when q<2. Tn this paper, we prove that Tis arc-parcyclic when p-;' 3q+3. We also find a useful result (Lemma VII) which deals with the longest cycle with a pair of arcs across it. 1. INTRODUCT.ION Since the regular tournament had been pron:d to be arc-pancyclic by Alspach [1], many further results about the arc-pancyclic property in tournaments have been found. In this paper, \ve shall show that a kind of tournaments has this property. The tournaments we'll consider is confined with a degree condition which was suggested in [2]. This degree condition is defined as follows : If tournament T of order p is said to satisfy O(p,q) conditon, where q is an integer, then every arc uv of T satifies that
Journal of Graph Theory, 2000
For two positive integers k, r , a (k, r)-coloring (or r-hued k-coloring) of a graph G is a prope... more For two positive integers k, r , a (k, r)-coloring (or r-hued k-coloring) of a graph G is a proper k-vertex-coloring such that every vertex v of degree dG(v) is adjacent to at least min{dG(v), r} distinct colors. The r-hued chromatic number, χr (G), is the smallest integer k for which G has a (k, r)-coloring. The maximum average degree of G, denoted bymad (G), equals max{2|E(H)|/|V (H)|: H is a subgraph of G}. In this paper, we prove the following results using thewell-known dischargingmethod. For a graph G, if mad(G) < 12 5 , then χ3(G) ≤ 6; if mad(G) < 7 3 , then χ3(G) ≤ 5; if G has no C5-components and mad(G) < 3 , then χ2(G) ≤ 4. © 2017 Elsevier B.V. All rights reserved.
Discrete Mathematics, 2018
Jaeger, Linial, Payan and Tarsi (JCTB, 1992) introduced the concept of group connectivity as a ge... more Jaeger, Linial, Payan and Tarsi (JCTB, 1992) introduced the concept of group connectivity as a generalization of nowhere-zero flow for graphs. In this paper, we introduce group connectivity for signed graphs and establish some fundamental properties. For a finite abelian group A, it is proved that an A-connected signed graph is a contractible configuration for Aflow problem of signed graphs. In addition, we give sufficient edge connectivity conditions for signed graphs to be A-connected and study the group connectivity of some families of signed graphs.
International Journal of Pattern Recognition and Artificial Intelligence, 2016
Signed networks with both positive and negative links have gained considerable attention over the... more Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlapping communities, where a node is allowed to belong to multiple communities, widely exist in many real-world networks. Another disadvantage of some existing algorithms is that the number of final clusters k should be an input of the clustering process. It may however be the case that we do not know k in advance. In this paper, to offer improvements to existing algorithms, we propose a new clust...
Circuit Double Cover of Graphs
Circuit Double Cover of Graphs
Circuit Double Cover of Graphs
Discrete Applied Mathematics, 2018
Abstract For two positive integers k , r , a ( k , r ) -coloring (or r -hued k -coloring) of a gr... more Abstract For two positive integers k , r , a ( k , r ) -coloring (or r -hued k -coloring) of a graph G is a proper k -vertex-coloring such that every vertex v of degree d G ( v ) is adjacent to at least min { d G ( v ) , r } distinct colors. The r -hued chromatic number, χ r ( G ) , is the smallest integer k for which G has a ( k , r ) -coloring. The maximum average degree of G , denoted by mad ( G ) , equals max { 2 | E ( H ) | ∕ | V ( H ) | : H is a subgraph of G } . In this paper, we prove the following results using the well-known discharging method. For a graph G , if mad ( G ) 12 5 , then χ 3 ( G ) ≤ 6 ; if mad ( G ) 7 3 , then χ 3 ( G ) ≤ 5 ; if G has no C 5 -components and mad ( G ) 8 3 , then χ 2 ( G ) ≤ 4 .
The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published ... more The Automatic Quasi-clique Merger algorithm is a new algorithm adapted from early work published under the name QCM (quasi-clique merger) [12, 11, 24, 19]. The AQCM algorithm performs hierarchical clustering in any data set for which there is an associated similarity measure quantifying the similarity of any data i and data j. Importantly, the method exhibits two valuable performance properties: 1) the ability to automatically return either a larger or smaller number of clusters depending on the inherent properties of the data rather than on a parameter 2) the ability to return a very large number of relatively small clusters automatically when such clusters are reasonably well defined in a data set. In this work we present the general idea of a quasi-clique agglomerative approach, provide the full details of the mathematical steps of the AQCM algorithm, and explain some of the motivation behind the new methodology. The main achievement of the new methodology is that the agglomerati...
European Journal of Combinatorics, 2021
Abstract It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfe... more Abstract It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. This conjecture has been verified for many families of snarks with small ( ≤ 5 ) cyclic edge-connectivity. An infinite family, denoted by S K , of cyclically 6-edge-connected superposition snarks was constructed in [European J. Combin. 2002] by Kochol. In this paper, the Berge–Fulkerson conjecture is verified for the family S K , and, furthermore, some larger families containing S K . This is the first paper about the Berge–Fulkerson conjecture for superposition snarks and cyclically 6-edge-connected snarks. Tutte’s integer flow and Catlin’s contractible configuration are applied here as the key methods.
Circuit Double Cover of Graphs
Journal of Combinatorial Theory, Series B, 2020
In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-z... more In 1983, Bouchet proposed a conjecture that every flow-admissible signed graph admits a nowhere-zero 6-flow. Bouchet himself proved that such signed graphs admit nowhere-zero 216-flows and Zýka further proved that such signed graphs admit nowherezero 30-flows. In this paper we show that every flow-admissible signed graph admits a nowhere-zero 11-flow.
Journal of Graph Theory, 2021
It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchi... more It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. Let G be a permutation graph with a 2‐factor F = { C 1 , C 2 } . A circuit C 0 is F ‐alternating if E ( C 0 ) ⧹ ( E ( C 1 ) ∪ E ( C 2 ) ) is a perfect matching of C 0 . A permutation graph G with a 2‐factor F = { C 1 , C 2 } is C ( 12 ) ‐linked if it contains an F ‐alternating circuit of length at most 12. It is proved in this paper that every C ( 12 ) ‐linked permutation graph is Berge–Fulkerson colorable. As an application, the conjecture is verified for some families of snarks constructed by Abreu et al., Brinkmann et al., and Hägglund et al.
Discrete Mathematics, Algorithms and Applications, 2020
The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertice... more The Wiener index of a connected graph is the sum of the distance of all pairs of distinct vertices. It was introduced by Wiener in 1947 to analyze some aspects of branching by fitting experimental data for several properties of alkane compounds. Denote by [Formula: see text] the set of unicyclic graphs with [Formula: see text] vertices and [Formula: see text] vertices of even degree. In this paper, we present a structural result on the graphs in [Formula: see text] with minimum Wiener index and completely characterize such graphs when [Formula: see text].
Journal of Graph Theory, 2018
A labeling of a digraph D with m arcs is a bijection from the set of arcs of D to {1,. .. , m}. A... more A labeling of a digraph D with m arcs is a bijection from the set of arcs of D to {1,. .. , m}. A labeling of D is antimagic if no two vertices in D have the same vertexsum, where the vertex-sum of a vertex u ∈ V (D) for a labeling is the sum of labels of all arcs entering u minus the sum of labels of all arcs leaving u. Motivated by the conjecture of Hartsfield and Ringel from 1990 on antimagic labelings of graphs, Hefetz, Mütze, and Schwartz [On antimagic directed graphs, J Graph Theory 64 (2010) 219-232] initiated the study of antimagic labelings of digraphs, and conjectured that every connected graph admits an antimagic orientation, where an orientation D of a graph G is antimagic if D has an antimagic labeling. It remained unknown whether every disjoint union of cycles admits an antimagic orientation. In this paper, we first answer this question in the positive by proving that every 2-regular graph has an antimagic orientation. We then show that for any integer d ≥ 2, every connected, 2d-regular graph has an antimagic orientation. Our technique is new.
Journal of Graph Theory, 2017
It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchi... more It is conjectured by Berge and Fulkerson that every bridgeless cubic graph has six perfect matchings such that each edge is contained in exactly two of them. Let be a cubic graph and = { 1 , … , } be a 2-factor of such that | | is odd if and only if ≤ 2 for some integer. The 2factor is (8)-linked if, for every ≤ , there is a circuit of length 8 with edge sequence 1 … 8 where 1 , 5 ∈ (2 −1) and 3 , 7 ∈ (2). And the cubic graph is (8)-linked if it contains a (8)-linked 2-factor. It is proved in this article that every (8)-linked cubic graph is Berge-Fulkerson colorable. It is also noticed that many classical families of snarks (including some high oddness snarks) are (8)-linked. Consequently, the Berge-Fulkerson conjecture is verified for these infinite families of snarks.
Graphs and Combinatorics, 2015
Your article is protected by copyright and all rights are held exclusively by Springer Japan. Thi... more Your article is protected by copyright and all rights are held exclusively by Springer Japan. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".
Circuit Double Cover of Graphs
Pattern Recognition Letters, 2011
In a graph theory model, clustering is the process of division of vertices into groups, with a hi... more In a graph theory model, clustering is the process of division of vertices into groups, with a higher density of edges within groups than between them. In this paper, we introduce a new clustering method for detecting such groups and use it to analyse some classic social networks. The new method has two distinguished features: non-binary hierarchical tree and the feature of overlapping clustering. A non-binary hierarchical tree is much smaller than the binary-trees constructed by most traditional methods and, therefore, it clearly highlights meaningful clusters which significantly reduces further manual efforts for cluster selections. The present method is tested by several bench mark data sets for which the community structure was known beforehand and the results indicate that it is a sensitive and accurate method for extracting community structure from social networks.
Journal of Information and Optimization Sciences, 1984
If a tournament T is said to satisfy O(p, q) condition, then d+(uHd-(v);;>p-q for each arc VII in... more If a tournament T is said to satisfy O(p, q) condition, then d+(uHd-(v);;>p-q for each arc VII in T, wha re p = I VeT) I , q is an integer. Let T be a tournament satis fying O{p,q) condition. Alspach [1] proved that T is arc-pancyclic when q= 1. Zhu and Tian [2] proved that T is arc-pancyclic when q<2. Tn this paper, we prove that Tis arc-parcyclic when p-;' 3q+3. We also find a useful result (Lemma VII) which deals with the longest cycle with a pair of arcs across it. 1. INTRODUCT.ION Since the regular tournament had been pron:d to be arc-pancyclic by Alspach [1], many further results about the arc-pancyclic property in tournaments have been found. In this paper, \ve shall show that a kind of tournaments has this property. The tournaments we'll consider is confined with a degree condition which was suggested in [2]. This degree condition is defined as follows : If tournament T of order p is said to satisfy O(p,q) conditon, where q is an integer, then every arc uv of T satifies that
Journal of Graph Theory, 2000