@article{MTMT:34820138,
	title = {Optimal strategies in fractional games: vertex cover and domination},
	url = {https://m2.mtmt.hu/api/publication/34820138},
	author = {Bujtás, Csilla and Rote, Günter and Tuza, Zsolt},
	doi = {10.26493/1855-3974.2771.4df},
	journal-iso = {ARS MATH CONTEMPOR},
	journal = {ARS MATHEMATICA CONTEMPORANEA},
	volume = {2024},
	unique-id = {34820138},
	issn = {1855-3966},
	year = {2024},
	eissn = {1855-3974},
	orcid-numbers = {Bujtás, Csilla/0000-0002-0511-5291}
}

@article{MTMT:34818984,
	title = {Extremal Graph Theoretic Questions for q-Ary Vectors},
	url = {https://m2.mtmt.hu/api/publication/34818984},
	author = {Patkós, Balázs and Tuza, Zsolt and Vizer, Máté},
	doi = {10.1007/s00373-024-02787-4},
	journal-iso = {GRAPH COMBINATOR},
	journal = {GRAPHS AND COMBINATORICS},
	volume = {40},
	unique-id = {34818984},
	issn = {0911-0119},
	abstract = {A q -graph H on n vertices is a set of vectors of length n with all entries from \{0,1,\dots ,q\} { 0 , 1 , ⋯ , q } and every vector (that we call a q -edge) having exactly two non-zero entries. The support of a q -edge {\textbf{x}} x is the pair S_{\textbf{x}} S x of indices of non-zero entries. We say that H is an s -copy of an ordinary graph F if |H|=|E(F)| | H | = | E ( F ) | , F is isomorphic to the graph with edge set \{S_{\textbf{x}}:{\textbf{x}}\in H\} { S x : x ∈ H } , and whenever v\in e,e'\in E(F) v ∈ e , e ′ ∈ E ( F ) , the entries with index corresponding to v in the q -edges corresponding to e and e' e ′ sum up to at least s . E.g., the q -edges (1, 3, 0, 0, 0), (0, 1, 0, 0, 3), and (3, 0, 0, 0, 1) form a 4-triangle. The Turán number \mathop {}\!\textrm{ex}(n,F,q,s) ex ( n , F , q , s ) is the maximum number of q -edges that a q -graph H on n vertices can have if it does not contain any s -copies of F . In the present paper, we determine the asymptotics of \mathop {}\!\textrm{ex}(n,F,q,q+1) ex ( n , F , q , q + 1 ) for many graphs F .},
	year = {2024},
	eissn = {1435-5914},
	orcid-numbers = {Patkós, Balázs/0000-0002-1651-2487}
}

@article{MTMT:34760346,
	title = {Connected Turán number of trees},
	url = {https://m2.mtmt.hu/api/publication/34760346},
	author = {Caro, Yair and Patkós, Balázs and Tuza, Zsolt},
	doi = {10.26493/1855-3974.3109.e4b},
	journal-iso = {ARS MATH CONTEMPOR},
	journal = {ARS MATHEMATICA CONTEMPORANEA},
	volume = {Manuscript Published 2023-10-03},
	unique-id = {34760346},
	issn = {1855-3966},
	abstract = {As a variant of the much studied Turán number, ex(n,F), the largest number of edges that an n-vertex F-free graph may contain, we introduce the connected Turán number exc(n,F), the largest number of edges that an n-vertex connected F-free graph may contain. We focus on the case where the forbidden graph is a tree. The celebrated conjecture of Erdős and Sós states that for any tree T, we have ex(n,T)≤(|T|−2)n2. We address the problem how much smaller exc(n,T) can be, what is the smallest possible ratio of exc(n,T) and (|T|−2)n2 as |T| grows. We also determine the exact value of exc(n,T) for small trees, in particular for all trees with at most six vertices. We introduce general constructions of connected T-free graphs based on graph parameters as longest path, matching number, branching number, etc.},
	year = {2024},
	eissn = {1855-3974},
	pages = {&},
	orcid-numbers = {Patkós, Balázs/0000-0002-1651-2487}
}

@article{MTMT:34397551,
	title = {Spectrum of 3-uniform 6- and 9-cycle systems over K (3) v − I},
	url = {https://m2.mtmt.hu/api/publication/34397551},
	author = {Keszler, Anita and Tuza, Zsolt},
	doi = {10.1016/j.disc.2023.113782},
	journal-iso = {DISCRETE MATH},
	journal = {DISCRETE MATHEMATICS},
	volume = {347},
	unique-id = {34397551},
	issn = {0012-365X},
	year = {2024},
	eissn = {1872-681X}
}

@article{MTMT:34162027,
	title = {Some exact results for regular Turán problems for all large orders},
	url = {https://m2.mtmt.hu/api/publication/34162027},
	author = {Gerbner, Dániel and Patkós, Balázs and Tuza, Zsolt and Vizer, Máté},
	doi = {10.1016/j.ejc.2023.103828},
	journal-iso = {EUR J COMBIN},
	journal = {EUROPEAN JOURNAL OF COMBINATORICS},
	volume = {117},
	unique-id = {34162027},
	issn = {0195-6698},
	year = {2024},
	eissn = {1095-9971},
	orcid-numbers = {Gerbner, Dániel/0000-0001-7080-2883; Patkós, Balázs/0000-0002-1651-2487}
}

@article{MTMT:34397516,
	title = {Gregarious Decompositions of Complete Equipartite Graphs and Related Structures},
	url = {https://m2.mtmt.hu/api/publication/34397516},
	author = {Tuza, Zsolt},
	doi = {10.3390/sym15122097},
	journal-iso = {SYMMETRY-BASEL},
	journal = {SYMMETRY (BASEL)},
	volume = {15},
	unique-id = {34397516},
	abstract = {In a finite mathematical structure with a given partition, a substructure is said to be gregarious if either it meets each partition class or it shares at most one element with each partition class. In this paper, we considered edge decompositions of graphs and hypergraphs into gregarious subgraphs and subhypergraphs. We mostly dealt with “complete equipartite” graphs and hypergraphs, where the vertex classes have the same size and precisely those edges or hyperedges of a fixed cardinality are present that do not contain more than one element from any class. Some related graph classes generated by product operations were also considered. The generalization to hypergraphs offers a wide open area for further research.},
	year = {2023},
	eissn = {2073-8994},
	pages = {2097}
}

@CONFERENCE{MTMT:34202465,
	title = {Egy téglalap-pakolási feladat, és megoldása különféle módszerekkel},
	url = {https://m2.mtmt.hu/api/publication/34202465},
	author = {Ábrahám, Gyula and Dósa, György and Olaj, Tomas Attila and Tuza, Zsolt and Lars, Magnus Hvattum},
	booktitle = {XXXV. Magyar Operációkutatás Konferencia},
	unique-id = {34202465},
	year = {2023},
	pages = {10},
	orcid-numbers = {Dósa, György/0000-0002-4909-6694}
}

@article{MTMT:34023034,
	title = {Vector sum-intersection theorems},
	url = {https://m2.mtmt.hu/api/publication/34023034},
	author = {Patkós, Balázs and Tuza, Zsolt and Vizer, Máté},
	doi = {10.1016/j.disc.2023.113506},
	journal-iso = {DISCRETE MATH},
	journal = {DISCRETE MATHEMATICS},
	volume = {346},
	unique-id = {34023034},
	issn = {0012-365X},
	year = {2023},
	eissn = {1872-681X},
	orcid-numbers = {Patkós, Balázs/0000-0002-1651-2487}
}

@article{MTMT:33843688,
	title = {Minimal Non-C-Perfect Hypergraphs with Circular Symmetry},
	url = {https://m2.mtmt.hu/api/publication/33843688},
	author = {Czaun, Péter Bence and Pusztai, Pál and Sebők, Levente and Tuza, Zsolt},
	doi = {10.3390/sym15051114},
	journal-iso = {SYMMETRY-BASEL},
	journal = {SYMMETRY (BASEL)},
	volume = {15},
	unique-id = {33843688},
	abstract = {In this research paper, we study 3-uniform hypergraphs H=(X,E) with circular symmetry. Two parameters are considered: the largest size α(H) of a set S⊂X not containing any edge E∈E, and the maximum number χ¯(H) of colors in a vertex coloring of H such that each E∈E contains two vertices of the same color. The problem considered here is to characterize those H in which the equality χ¯(H′)=α(H′) holds for every induced subhypergraph H′=(X′,E′) of H. A well-known objection against χ¯(H′)=α(H′) is where ∩E∈E′E=1, termed “monostar”. Steps toward a solution to this approach is to investigate the properties of monostar-free structures. All such H are completely identified up to 16 vertices, with the aid of a computer. Most of them can be shown to satisfy χ¯(H)=α(H), and the few exceptions contain one or both of two specific induced subhypergraphs H5⥁, H6⥁ on five and six vertices, respectively, both with χ¯=2 and α=3. Furthermore, a general conjecture is raised for hypergraphs of prime orders.},
	year = {2023},
	eissn = {2073-8994},
	orcid-numbers = {Czaun, Péter Bence/0009-0007-4268-8340}
}

@article{MTMT:33569160,
	title = {The board packing problem},
	url = {https://m2.mtmt.hu/api/publication/33569160},
	author = {Ábrahám, Gyula and Dósa, György and Lars, Magnus Hvattum and Olaj, Tomas Attila and Tuza, Zsolt},
	doi = {10.1016/j.ejor.2023.01.030},
	journal-iso = {EJOR},
	journal = {EUROPEAN JOURNAL OF OPERATIONAL RESEARCH},
	volume = {308},
	unique-id = {33569160},
	issn = {0377-2217},
	abstract = {We introduce the board packing problem (BoPP). In this problem we are given a rectangular board with a given number of rows and columns. Each position of the board has an integer value representing a gain, or revenue, that is obtained if the position is covered. A set of rectangles is also given, each with a given size and cost. The objective is to purchase some rectangles to place on the board so as to maximize the profit, which is the sum of the gain values of the covered cells minus the total cost of purchased rectangles. This problem subsumes several natural optimization problems that arise in practice. A mixedinteger programming model for the BoPP problem is provided, along with a proof that BoPP is NP -hard by reduction from the satisfiability problem. An evolutionary algorithm is also developed that can solve large instances of BoPP. We introduce benchmark instances and make extensive computer examinations.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )},
	year = {2023},
	eissn = {1872-6860},
	pages = {1056-1073},
	orcid-numbers = {Dósa, György/0000-0002-4909-6694}
}