Hung-lin Fu - Academia.edu (original) (raw)
Papers by Hung-lin Fu
Discrete Mathematics, Algorithms and Applications, Oct 1, 2017
A set of vertices of a graph whose removal leaves an acyclic graph is referred as a decycling set... more A set of vertices of a graph whose removal leaves an acyclic graph is referred as a decycling set, or a feedback vertex set, of the graph. The minimum cardinality of a decycling set of a graph [Formula: see text] is referred to as the decycling number of [Formula: see text]. For [Formula: see text], the generalized de Bruijn digraph [Formula: see text] is defined by congruence equations as follows: [Formula: see text] and [Formula: see text]. In this paper, we give a systematic method to find a decycling set of [Formula: see text] and give a new upper bound that improve the best known results. By counting the number of vertex-disjoint cycles with the idea of constrained necklaces, we obtain new lower bounds on the decycling number of generalized de Bruijn digraphs.
Ars Combinatoria Waterloo Then Winnipeg, 2004
Lecture notes in social networks, Dec 12, 2018
arXiv (Cornell University), Oct 29, 2021
The total chromatic number, χ ′′ (G) is the minimum number of colors which need to be assigned to... more The total chromatic number, χ ′′ (G) is the minimum number of colors which need to be assigned to obtain a total coloring of the graph G. The Total Coloring Conjecture (TCC) made independently by Behzad and Vizing that for any graph, χ ′′ (G) ≤ ∆(G)+ 2, where ∆(G) represents the maximum degree of G. In this paper we obtained the total chromatic number for some classes of four regular circulant graphs.
Discrete Mathematics, Algorithms and Applications, Dec 7, 2020
The total chromatic number [Formula: see text] is the least number of colors needed to color the ... more The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles.
Journal of Graph Theory, Feb 1, 1997
A (k; g)-graph is a k-regular graph with girth g. Let f (k; g) be the smallest integer ν such the... more A (k; g)-graph is a k-regular graph with girth g. Let f (k; g) be the smallest integer ν such there exists a (k; g)-graph with ν vertices. A (k; g)-cage is a (k; g)-graph with f (k; g) vertices. In this paper we prove that the cages are monotonic in that f (k; g 1) < f(k; g 2) for all k ≥ 3 and 3 ≤ g 1 < g 2. We use this to prove that (k; g)-cages are 2-connected, and if k = 3 then their connectivity is k.
Journal of Combinatorial Optimization, Nov 4, 2020
In Classical group testing, one is given a population of n items N which contains some defective ... more In Classical group testing, one is given a population of n items N which contains some defective d items inside. A group test (pool) is a test on a subset of N. Under the circumstance of no errors, a test is negative if the testing pool contains no defective items and the test is positive if the testing pool contains at least one defective item but we don't know which one. The goal is to find all defectives by using as less tests as possible, mainly to minimize the number of tests (in the worst case situation). Let M(d, n) denote the minimum number of tests in the worst case situation where |N | = n and d is the number of defectives. In this paper, we focus on estimating M(d, n) and obtain a better result than known ones in various cases of d and n.
Journal of Combinatorial Designs, 2006
Discrete Applied Mathematics, Dec 1, 2017
In this paper, we derive bounds on the optimal average information ratio of the access structures... more In this paper, we derive bounds on the optimal average information ratio of the access structures based on general graphs and investigate the value of the ratio for unicycle graphs and some bipartite graphs. We determine the exact values of this ratio for some infinite classes of bipartite graphs and unicycle graphs. This extends previous results. We also provide good bounds on the optimal average information ratio for all unicycle graphs.
Let G be a graph with (" : ') edges. We say G has an ascending subgraph decomposition (ASD) if th... more Let G be a graph with (" : ') edges. We say G has an ascending subgraph decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G,, G,,. , G, such that IE(G,)I = i (for i = 1, 2,. . , n) and G, is isomorphic to a subgraph of G,+r for i = 1,2,. . , n-1. In this note, we prove that if G is a graph of maximum degree d C [(n + 1)/2j on (" l ') edges, then G has an ASD. Moreover, we show that if d s [(n-1)/2], then G has an ASD with each member a matching. Subsequently, we also verify that every regular graph of degree a prime power has an ASD.
Australas. J Comb., 1992
We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the foll... more We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the following results: (i) maXl<t<rn min{l mn J, t(m + n-1)t 2 + I}-t ~ w(Krn X Kn} >{m+n-~-2n-f-l if n > m > 2. m 1 if n > m = 2 or m n> 2 ; and Moreover, for m 2,3, the bounds give the exact achromatic numbers W(Krn X Kn} if not both m and n are equal to 2. (ii) W(G 1 X G 2) ~ W(Krn X Kn} if w(Gt) m and w(G 2) n.
Asia-Pacific Conference on Communications, Dec 1, 2008
The paper proposes an improved module-based substitution method for image hiding. The method has ... more The paper proposes an improved module-based substitution method for image hiding. The method has the following characteristics: (1) The extracted data are lossless. (2) Each k-bit datum is hidden in a pixel of the host image, and the gray-value distortion is not larger than 2k-1 for most of the pixels. (3) If it is compared with reported lossless Least-Significant-Bits (LSB)
Utilitas Mathematica, Nov 1, 2007
Journal of Discrete Mathematical Sciences and Cryptography, Nov 17, 2017
Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both ... more Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both u and υ are even, where F1 is a 1-factor of Kυ and F2 is a 1-factor of Ku with F2⊆F1. In this paper, we study the existence problem of m-cycle design of Gυu. By using direct and recurssive constructions, we obtain several new m-cycle design of Gυu.
Ars Combinatoria, Oct 1, 1999
Tamkang Journal of Mathematics, Dec 1, 1990
Tamkang Journal of Mathematics, Mar 1, 1996
This paper presents a simple method for constructing universally opti mal block designs with nest... more This paper presents a simple method for constructing universally opti mal block designs with nested rows and columns for number of treatments greater than the number of columns. By allowing a near maximum trace in l!.v ,p.q, we pro pose an initial row-column design to achieve a completely symmetric information matrix in much lesser than v! blocks. This constructive method is then extended to the case when balanced incomplete block design is given in the columns. where r~is the v x v diagonal matrix of replication numbers of the treatments, Nd1 and Nn2 are the treatment-row and treatment-column incidence matrices, and 凶 ＝乜 ] is
arXiv (Cornell University), May 8, 2019
Let G = (V, E) be a simple undirected graph. G is a circulant graph defined on V = Zn with differ... more Let G = (V, E) be a simple undirected graph. G is a circulant graph defined on V = Zn with difference set D ⊆ {1, 2,. .. , ⌊ n 2 ⌋} provided two vertices i and j in Zn are adjacent if and only if min{|i−j|, n−|i−j|} ∈ D. For convenience, we use G(n; D) to denote such a circulant graph. A function f : V (G) → N∪{0} is an integer {k}-domination function if for each v ∈ V (G), u∈N G [v] f (u) ≥ k. By considering all {k}-domination functions f , the minimum value of v∈V (G) f (v) is the {k}-domination number of G, denoted by γ k (G). In this paper, we prove that if D = {1, 2,. .. , t}, 1 ≤ t ≤ n−1 2 , then the integer {k}-domination number of G(n; D) is ⌈ kn 2t+1 ⌉.
Journal of Combinatorial Designs, 2005
In this paper, the necessary and sufficient conditions for the existence of cyclic 2qcycle and m-... more In this paper, the necessary and sufficient conditions for the existence of cyclic 2qcycle and m-cycle systems of the complete graph with q a prime power and 3 m 32 are given.
Discrete Mathematics, Algorithms and Applications, Oct 1, 2017
A set of vertices of a graph whose removal leaves an acyclic graph is referred as a decycling set... more A set of vertices of a graph whose removal leaves an acyclic graph is referred as a decycling set, or a feedback vertex set, of the graph. The minimum cardinality of a decycling set of a graph [Formula: see text] is referred to as the decycling number of [Formula: see text]. For [Formula: see text], the generalized de Bruijn digraph [Formula: see text] is defined by congruence equations as follows: [Formula: see text] and [Formula: see text]. In this paper, we give a systematic method to find a decycling set of [Formula: see text] and give a new upper bound that improve the best known results. By counting the number of vertex-disjoint cycles with the idea of constrained necklaces, we obtain new lower bounds on the decycling number of generalized de Bruijn digraphs.
Ars Combinatoria Waterloo Then Winnipeg, 2004
Lecture notes in social networks, Dec 12, 2018
arXiv (Cornell University), Oct 29, 2021
The total chromatic number, χ ′′ (G) is the minimum number of colors which need to be assigned to... more The total chromatic number, χ ′′ (G) is the minimum number of colors which need to be assigned to obtain a total coloring of the graph G. The Total Coloring Conjecture (TCC) made independently by Behzad and Vizing that for any graph, χ ′′ (G) ≤ ∆(G)+ 2, where ∆(G) represents the maximum degree of G. In this paper we obtained the total chromatic number for some classes of four regular circulant graphs.
Discrete Mathematics, Algorithms and Applications, Dec 7, 2020
The total chromatic number [Formula: see text] is the least number of colors needed to color the ... more The total chromatic number [Formula: see text] is the least number of colors needed to color the vertices and edges of a graph [Formula: see text] such that no incident or adjacent elements (vertices or edges) receive the same color. Behzad and Vizing proposed a well-known total coloring conjecture (TCC): [Formula: see text], where [Formula: see text] is the maximum degree of [Formula: see text]. For the powers of cycles, Campos and de Mello proposed the following conjecture: Let [Formula: see text] denote the graphs of powers of cycles of order [Formula: see text] and length [Formula: see text] with [Formula: see text]. Then, [Formula: see text] In this paper, we prove the Campos and de Mello’s conjecture for some classes of powers of cycles. Also, we prove the TCC for complement of powers of cycles.
Journal of Graph Theory, Feb 1, 1997
A (k; g)-graph is a k-regular graph with girth g. Let f (k; g) be the smallest integer ν such the... more A (k; g)-graph is a k-regular graph with girth g. Let f (k; g) be the smallest integer ν such there exists a (k; g)-graph with ν vertices. A (k; g)-cage is a (k; g)-graph with f (k; g) vertices. In this paper we prove that the cages are monotonic in that f (k; g 1) < f(k; g 2) for all k ≥ 3 and 3 ≤ g 1 < g 2. We use this to prove that (k; g)-cages are 2-connected, and if k = 3 then their connectivity is k.
Journal of Combinatorial Optimization, Nov 4, 2020
In Classical group testing, one is given a population of n items N which contains some defective ... more In Classical group testing, one is given a population of n items N which contains some defective d items inside. A group test (pool) is a test on a subset of N. Under the circumstance of no errors, a test is negative if the testing pool contains no defective items and the test is positive if the testing pool contains at least one defective item but we don't know which one. The goal is to find all defectives by using as less tests as possible, mainly to minimize the number of tests (in the worst case situation). Let M(d, n) denote the minimum number of tests in the worst case situation where |N | = n and d is the number of defectives. In this paper, we focus on estimating M(d, n) and obtain a better result than known ones in various cases of d and n.
Journal of Combinatorial Designs, 2006
Discrete Applied Mathematics, Dec 1, 2017
In this paper, we derive bounds on the optimal average information ratio of the access structures... more In this paper, we derive bounds on the optimal average information ratio of the access structures based on general graphs and investigate the value of the ratio for unicycle graphs and some bipartite graphs. We determine the exact values of this ratio for some infinite classes of bipartite graphs and unicycle graphs. This extends previous results. We also provide good bounds on the optimal average information ratio for all unicycle graphs.
Let G be a graph with (" : ') edges. We say G has an ascending subgraph decomposition (ASD) if th... more Let G be a graph with (" : ') edges. We say G has an ascending subgraph decomposition (ASD) if the edge set of G can be partitioned into n sets generating graphs G,, G,,. , G, such that IE(G,)I = i (for i = 1, 2,. . , n) and G, is isomorphic to a subgraph of G,+r for i = 1,2,. . , n-1. In this note, we prove that if G is a graph of maximum degree d C [(n + 1)/2j on (" l ') edges, then G has an ASD. Moreover, we show that if d s [(n-1)/2], then G has an ASD with each member a matching. Subsequently, we also verify that every regular graph of degree a prime power has an ASD.
Australas. J Comb., 1992
We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the foll... more We study the achromatic number of the Cartesian product of graphs G 1 and G 2 and obtain the following results: (i) maXl<t<rn min{l mn J, t(m + n-1)t 2 + I}-t ~ w(Krn X Kn} >{m+n-~-2n-f-l if n > m > 2. m 1 if n > m = 2 or m n> 2 ; and Moreover, for m 2,3, the bounds give the exact achromatic numbers W(Krn X Kn} if not both m and n are equal to 2. (ii) W(G 1 X G 2) ~ W(Krn X Kn} if w(Gt) m and w(G 2) n.
Asia-Pacific Conference on Communications, Dec 1, 2008
The paper proposes an improved module-based substitution method for image hiding. The method has ... more The paper proposes an improved module-based substitution method for image hiding. The method has the following characteristics: (1) The extracted data are lossless. (2) Each k-bit datum is hidden in a pixel of the host image, and the gray-value distortion is not larger than 2k-1 for most of the pixels. (3) If it is compared with reported lossless Least-Significant-Bits (LSB)
Utilitas Mathematica, Nov 1, 2007
Journal of Discrete Mathematical Sciences and Cryptography, Nov 17, 2017
Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both ... more Abstract Let Gυu denote the graph Kυ\Ku if both u and υ are odd, and (Kυ – F1)\(Ku – F2) if both u and υ are even, where F1 is a 1-factor of Kυ and F2 is a 1-factor of Ku with F2⊆F1. In this paper, we study the existence problem of m-cycle design of Gυu. By using direct and recurssive constructions, we obtain several new m-cycle design of Gυu.
Ars Combinatoria, Oct 1, 1999
Tamkang Journal of Mathematics, Dec 1, 1990
Tamkang Journal of Mathematics, Mar 1, 1996
This paper presents a simple method for constructing universally opti mal block designs with nest... more This paper presents a simple method for constructing universally opti mal block designs with nested rows and columns for number of treatments greater than the number of columns. By allowing a near maximum trace in l!.v ,p.q, we pro pose an initial row-column design to achieve a completely symmetric information matrix in much lesser than v! blocks. This constructive method is then extended to the case when balanced incomplete block design is given in the columns. where r~is the v x v diagonal matrix of replication numbers of the treatments, Nd1 and Nn2 are the treatment-row and treatment-column incidence matrices, and 凶 ＝乜 ] is
arXiv (Cornell University), May 8, 2019
Let G = (V, E) be a simple undirected graph. G is a circulant graph defined on V = Zn with differ... more Let G = (V, E) be a simple undirected graph. G is a circulant graph defined on V = Zn with difference set D ⊆ {1, 2,. .. , ⌊ n 2 ⌋} provided two vertices i and j in Zn are adjacent if and only if min{|i−j|, n−|i−j|} ∈ D. For convenience, we use G(n; D) to denote such a circulant graph. A function f : V (G) → N∪{0} is an integer {k}-domination function if for each v ∈ V (G), u∈N G [v] f (u) ≥ k. By considering all {k}-domination functions f , the minimum value of v∈V (G) f (v) is the {k}-domination number of G, denoted by γ k (G). In this paper, we prove that if D = {1, 2,. .. , t}, 1 ≤ t ≤ n−1 2 , then the integer {k}-domination number of G(n; D) is ⌈ kn 2t+1 ⌉.
Journal of Combinatorial Designs, 2005
In this paper, the necessary and sufficient conditions for the existence of cyclic 2qcycle and m-... more In this paper, the necessary and sufficient conditions for the existence of cyclic 2qcycle and m-cycle systems of the complete graph with q a prime power and 3 m 32 are given.