Ervin Győri - Academia.edu (original) (raw)

Papers by Ervin Győri

arXiv (Cornell University), Jul 13, 2023

The planar Turán number, exP(n, H), is the maximum number of edges in an n-vertex planar graph wh... more The planar Turán number, exP(n, H), is the maximum number of edges in an n-vertex planar graph which does not contain H as a subgraph. The topic of extremal planar graphs was initiated by Dowden (2016). He obtained sharp upper bound for both exP (n, C4) and exP (n, C5). Later on, D. Ghosh et al. obtained sharp upper bound of exP(n, C6) and proposed a conjecture on exP (n, C k ) for 7 ≤ k ≤ 10. In this paper, we give a sharp upper bound exP (n, C7) ≤ 18 7 n -48 7 , which satisfies the conjecture of D. Ghosh et al. It turns out that this upper bound is also sharp for exP(n, {K4, C7}), the maximum number of edges in an n-vertex planar graph which does not contain K4 or C7 as a subgraph.

Extensions of the Erd\H{o}s-Gallai theorem for general hypergraphs are well studied. In this work... more Extensions of the Erd\H{o}s-Gallai theorem for general hypergraphs are well studied. In this work, we prove the extension of the Erd\H{o}s-Gallai theorem for linear hypergraphs. In particular, we show that the number of hyperedges in an nnn-vertex 333-uniform linear hypergraph, without a Berge path of length kkk as a subgraph is at most frac(k−1)6n\frac{(k-1)}{6}nfrac(k−1)6n for kgeq4k\geq 4kgeq4. This is an extended abstract for EUROCOMB23 of the manuscript arXiv:2211.16184.

arXiv (Cornell University), Dec 1, 2019

We refine two results of Jiang, Shao and Vesel on the L(2, 1)-labeling number λ of the Cartesian ... more We refine two results of Jiang, Shao and Vesel on the L(2, 1)-labeling number λ of the Cartesian and the strong product of two oriented cycles. For the Cartesian product, we compute the exact value of λ( -→ Cm -→ Cn) for m, n ≥ 40; in the case of strong product, we either compute the exact value or establish a gap of size one for λ( -→ Cm -→ Cn) for m, n ≥ 48.

A pályázatban három kutató vett részt: T. Sós Vera, akadémikus, Győri Ervin, a tudományok doktora... more A pályázatban három kutató vett részt: T. Sós Vera, akadémikus, Győri Ervin, a tudományok doktora, és pályázatvezetőként én, Simonovits Miklós (akad. lev tag). Célunk elsősorban a korábbi kutatásaink folytatása, illetve az azokból adódó újabb kérdések vizsgálata volt. Az általunk vizsgált, szerteágazó, de mégis szorosan összefüggő területről kiemelnénk az alábbiakat. 1. Klasszikus extremális gráfelméleti és Ramsey elméleti kérdések, közönséges gráfokra, ill. hipergráfelméleti extremális gráfelméleti problémák vizsgálata, hipergráfelméleti Ramsey problémák. 2. Hipergráfelméleti Ramsey és extrém problémák kapcsolata. 3. Ramsey-Turán típusú hipergráf problémák. 4. Erdős-Kleitman-Rothschild típusú kérdések vizsgálata. 5. Gráfsorozatok konvergenciájának, gráfok metrikus terének értelmezése, a különböző konvergenciafogalmak ekvivalenciái. 6. Előbbi alkalmazásai, gráfok lokális és globális tulajdonságai kapcsolatainak vizsgálata, parameter testing. brought to you by CORE View metadata, citation and similar papers at core.ac.uk

arXiv (Cornell University), Jan 11, 2015

We consider the following generalization of graph packing. Let G 1 = (V 1 , E 1 ) and G 2 = (V 2 ... more We consider the following generalization of graph packing. Let G 1 = (V 1 , E 1 ) and G 2 = (V 2 , E 2 ) be graphs of order n and We extend the classical results of Sauer and Spencer and Bollobás and Eldridge on packing of graphs with small sizes or maximum degrees to the setting of list packing. In particular, we extend the well-known Bollobás-Eldridge Theorem, ) packs or is one of 7 possible exceptions. Hopefully, the concept of list packing will help to solve some problems on ordinary graph packing, as the concept of list coloring did for ordinary coloring.

Combinatorica, Mar 1, 1989

Etablissement d'une borne superieure du nombre de cycles de longueur 5 dans un graphe d'o... more Etablissement d'une borne superieure du nombre de cycles de longueur 5 dans un graphe d'ordre n sans triangles, en relation avec une conjecture de P. Erdos

arXiv (Cornell University), Aug 27, 2016

Let C be a clique covering for E(G) and let v be a vertex of G. The valency of vertex v (with res... more Let C be a clique covering for E(G) and let v be a vertex of G. The valency of vertex v (with respect to C), denoted by val C (v), is the number of cliques in C containing v. The local clique cover number of G, denoted by lcc(G), is defined as the smallest integer k, for which there exists a clique covering for E(G) such that val C (v) is at most k, for every vertex v ∈ V (G). In this paper, among other results, we prove that if G is a claw-free graph, then lcc(G) + χ(G) ≤ n + 1.

Cambridge University Press eBooks, Apr 5, 2001

Discrete Mathematics, May 1, 1992

Gyari, E. and M.D. Plummer, The Cartesian product of a k-extendable and an I-extendable graph is ... more Gyari, E. and M.D. Plummer, The Cartesian product of a k-extendable and an I-extendable graph is (k + I + I)-extendable, Discrete Mathematics 101 (1992) 87-96.

We prove that the ratio of the minimum number of rectangles covering a simply com~ected board (po... more We prove that the ratio of the minimum number of rectangles covering a simply com~ected board (polyomino) B and the maximum number of points in B no two of which are contained in a common rectangle is less than 2.

Cambridge University Press eBooks, Apr 5, 2001

Extremal Graph Theory is the study of how large the edge density of graphs can be while still exc... more Extremal Graph Theory is the study of how large the edge density of graphs can be while still excluding certain forbidden substructures. Such problems are also known as Turan type problems. We are interested in the number of edges a finite graph can have while exculding certain cycles. One can ask similar questions about the size of hypergraphs avoiding certain cycles. (Of course, it is not immeadiately clear how a cycle should be defined in the hypergraph case.) Interestingly, the two problems seem to be quite related and studying C5-free hypergraphs has led to results in graph theory as well.

arXiv (Cornell University), Jun 10, 2015

We show the quarter of a century old conjecture that every K 4 -free graph with n vertices and ⌊n... more We show the quarter of a century old conjecture that every K 4 -free graph with n vertices and ⌊n 2 /4⌋ + k edges contains k pairwise edge disjoint triangles.

arXiv (Cornell University), Dec 27, 2018

Springer eBooks, May 27, 2008

Hungarian mathematics has always been known for discrete mathematics, including combinatorial num... more Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, combinatorial geometry as well. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives a very good overview of recent trends and results in a large part of combinatorics and related topics, and offers an interesting reading for experienced specialists as well as to young researchers and students.

arXiv (Cornell University), Jul 9, 2023

arXiv (Cornell University), Dec 5, 2019

Bolyai Society mathematical studies, 2006

This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes surv... more This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research

arXiv (Cornell University), Sep 17, 2015

arXiv (Cornell University), Aug 29, 2022

arXiv (Cornell University), Jul 13, 2023

The planar Turán number, exP(n, H), is the maximum number of edges in an n-vertex planar graph wh... more The planar Turán number, exP(n, H), is the maximum number of edges in an n-vertex planar graph which does not contain H as a subgraph. The topic of extremal planar graphs was initiated by Dowden (2016). He obtained sharp upper bound for both exP (n, C4) and exP (n, C5). Later on, D. Ghosh et al. obtained sharp upper bound of exP(n, C6) and proposed a conjecture on exP (n, C k ) for 7 ≤ k ≤ 10. In this paper, we give a sharp upper bound exP (n, C7) ≤ 18 7 n -48 7 , which satisfies the conjecture of D. Ghosh et al. It turns out that this upper bound is also sharp for exP(n, {K4, C7}), the maximum number of edges in an n-vertex planar graph which does not contain K4 or C7 as a subgraph.

Extensions of the Erd\H{o}s-Gallai theorem for general hypergraphs are well studied. In this work... more Extensions of the Erd\H{o}s-Gallai theorem for general hypergraphs are well studied. In this work, we prove the extension of the Erd\H{o}s-Gallai theorem for linear hypergraphs. In particular, we show that the number of hyperedges in an nnn-vertex 333-uniform linear hypergraph, without a Berge path of length kkk as a subgraph is at most frac(k−1)6n\frac{(k-1)}{6}nfrac(k−1)6n for kgeq4k\geq 4kgeq4. This is an extended abstract for EUROCOMB23 of the manuscript arXiv:2211.16184.

arXiv (Cornell University), Dec 1, 2019

We refine two results of Jiang, Shao and Vesel on the L(2, 1)-labeling number λ of the Cartesian ... more We refine two results of Jiang, Shao and Vesel on the L(2, 1)-labeling number λ of the Cartesian and the strong product of two oriented cycles. For the Cartesian product, we compute the exact value of λ( -→ Cm -→ Cn) for m, n ≥ 40; in the case of strong product, we either compute the exact value or establish a gap of size one for λ( -→ Cm -→ Cn) for m, n ≥ 48.

A pályázatban három kutató vett részt: T. Sós Vera, akadémikus, Győri Ervin, a tudományok doktora... more A pályázatban három kutató vett részt: T. Sós Vera, akadémikus, Győri Ervin, a tudományok doktora, és pályázatvezetőként én, Simonovits Miklós (akad. lev tag). Célunk elsősorban a korábbi kutatásaink folytatása, illetve az azokból adódó újabb kérdések vizsgálata volt. Az általunk vizsgált, szerteágazó, de mégis szorosan összefüggő területről kiemelnénk az alábbiakat. 1. Klasszikus extremális gráfelméleti és Ramsey elméleti kérdések, közönséges gráfokra, ill. hipergráfelméleti extremális gráfelméleti problémák vizsgálata, hipergráfelméleti Ramsey problémák. 2. Hipergráfelméleti Ramsey és extrém problémák kapcsolata. 3. Ramsey-Turán típusú hipergráf problémák. 4. Erdős-Kleitman-Rothschild típusú kérdések vizsgálata. 5. Gráfsorozatok konvergenciájának, gráfok metrikus terének értelmezése, a különböző konvergenciafogalmak ekvivalenciái. 6. Előbbi alkalmazásai, gráfok lokális és globális tulajdonságai kapcsolatainak vizsgálata, parameter testing. brought to you by CORE View metadata, citation and similar papers at core.ac.uk

arXiv (Cornell University), Jan 11, 2015

We consider the following generalization of graph packing. Let G 1 = (V 1 , E 1 ) and G 2 = (V 2 ... more We consider the following generalization of graph packing. Let G 1 = (V 1 , E 1 ) and G 2 = (V 2 , E 2 ) be graphs of order n and We extend the classical results of Sauer and Spencer and Bollobás and Eldridge on packing of graphs with small sizes or maximum degrees to the setting of list packing. In particular, we extend the well-known Bollobás-Eldridge Theorem, ) packs or is one of 7 possible exceptions. Hopefully, the concept of list packing will help to solve some problems on ordinary graph packing, as the concept of list coloring did for ordinary coloring.

Combinatorica, Mar 1, 1989

Etablissement d'une borne superieure du nombre de cycles de longueur 5 dans un graphe d'o... more Etablissement d'une borne superieure du nombre de cycles de longueur 5 dans un graphe d'ordre n sans triangles, en relation avec une conjecture de P. Erdos

arXiv (Cornell University), Aug 27, 2016

Let C be a clique covering for E(G) and let v be a vertex of G. The valency of vertex v (with res... more Let C be a clique covering for E(G) and let v be a vertex of G. The valency of vertex v (with respect to C), denoted by val C (v), is the number of cliques in C containing v. The local clique cover number of G, denoted by lcc(G), is defined as the smallest integer k, for which there exists a clique covering for E(G) such that val C (v) is at most k, for every vertex v ∈ V (G). In this paper, among other results, we prove that if G is a claw-free graph, then lcc(G) + χ(G) ≤ n + 1.

Cambridge University Press eBooks, Apr 5, 2001

Discrete Mathematics, May 1, 1992

Gyari, E. and M.D. Plummer, The Cartesian product of a k-extendable and an I-extendable graph is ... more Gyari, E. and M.D. Plummer, The Cartesian product of a k-extendable and an I-extendable graph is (k + I + I)-extendable, Discrete Mathematics 101 (1992) 87-96.

We prove that the ratio of the minimum number of rectangles covering a simply com~ected board (po... more We prove that the ratio of the minimum number of rectangles covering a simply com~ected board (polyomino) B and the maximum number of points in B no two of which are contained in a common rectangle is less than 2.

Cambridge University Press eBooks, Apr 5, 2001

Extremal Graph Theory is the study of how large the edge density of graphs can be while still exc... more Extremal Graph Theory is the study of how large the edge density of graphs can be while still excluding certain forbidden substructures. Such problems are also known as Turan type problems. We are interested in the number of edges a finite graph can have while exculding certain cycles. One can ask similar questions about the size of hypergraphs avoiding certain cycles. (Of course, it is not immeadiately clear how a cycle should be defined in the hypergraph case.) Interestingly, the two problems seem to be quite related and studying C5-free hypergraphs has led to results in graph theory as well.

arXiv (Cornell University), Jun 10, 2015

We show the quarter of a century old conjecture that every K 4 -free graph with n vertices and ⌊n... more We show the quarter of a century old conjecture that every K 4 -free graph with n vertices and ⌊n 2 /4⌋ + k edges contains k pairwise edge disjoint triangles.

arXiv (Cornell University), Dec 27, 2018

Springer eBooks, May 27, 2008

Hungarian mathematics has always been known for discrete mathematics, including combinatorial num... more Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, combinatorial geometry as well. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives a very good overview of recent trends and results in a large part of combinatorics and related topics, and offers an interesting reading for experienced specialists as well as to young researchers and students.

arXiv (Cornell University), Jul 9, 2023

arXiv (Cornell University), Dec 5, 2019

Bolyai Society mathematical studies, 2006

This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes surv... more This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research

arXiv (Cornell University), Sep 17, 2015

arXiv (Cornell University), Aug 29, 2022