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Some results on the multipartite Ramsey numbers mj(C3,Cm,n1K2,n2K2,…,niK2) [PDF]
Heliyon, 2022 The graph Kj×t is a graph which is complete and multipartite which includes j partite sets and t vertices in each partite set. The multipartite Ramsey number (M-R-number) mj(G1,G2,…,Gn) is the smallest integer t for the mentioned graphs G1,G2,…,Gn, in a ...
Yaser Rowshan +2 more
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Ramsey and Gallai-Ramsey numbers for forests
Discussiones Mathematicae Graph TheorySummary: Given two non-empty graphs \(G,H\) and a positive integer \(k\), the Gallai-Ramsey number \(\operatorname{gr}_k(G:H)\) is defined as the minimum integer \(N\) such that for all \(n\geq N\), every \(k\)-edge-coloring of \(K_n\) contains either a rainbow copy of \(G\) or a monochromatic copy of \(H\).
Yujia Gao +3 more
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Journal of Combinatorial Theory Series B, 2017 Given a labeled graph $H$ with vertex set $\{1, 2,\ldots,n\}$, the ordered Ramsey number ...
David Conlon +2 more
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Ramsey and Gallai-Ramsey Number for Wheels [PDF]
Graphs and Combinatorics, 2022 arXiv admin note: text overlap with arXiv:1809.10298, arXiv:1902 ...
Yaping Mao +3 more
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A Proof of a Conjecture on Bipartite Ramsey Numbers B(2,2,3)
Mathematics, 2022 The bipartite Ramsey number B(n1,n2,…,nt) is the least positive integer b, such that any coloring of the edges of Kb,b with t colors will result in a monochromatic copy of Kni,ni in the i-th color, for some i, 1≤i≤t.
Yaser Rowshan +2 more
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Multicolor star-critical Ramsey numbers and Ramsey-good graphs
Electronic Journal of Graph Theory and Applications, 2022 This paper seeks to develop the multicolor version of star-critical Ramsey numbers, which serve as a measure of the strength of the corresponding Ramsey numbers. We offer several general theorems, some of which focus on Ramsey-good cases (i.e., cases in
Mark Rowland Budden, Elijah DeJonge
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The Size, Multipartite Ramsey Numbers for nK2 Versus Path–Path and Cycle
Mathematics, 2021 For given graphs G1,G2,…,Gn and any integer j, the size of the multipartite Ramsey number mj(G1,G2,…,Gn) is the smallest positive integer t such that any n-coloring of the edges of Kj×t contains a monochromatic copy of Gi in color i for some i, 1≤i≤n ...
Yaser Rowshan +2 more
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Anti-Ramsey Hypergraph Numbers
Electronic Journal of Graph Theory and Applications, 2021 The anti-Ramsey number arn(H) of an r-uniform hypergraph is the maximum number of colors that can be used to color the hyperedges of a complete r-uniform hypergraph on n vertices without producing a rainbow copy of H.
Mark Budden, William Stiles
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Constrained Ramsey Numbers [PDF]
Electronic Notes in Discrete Mathematics, 2007 For two graphs S and T, the constrained Ramsey number f(S, T) is the minimum n such that every edge colouring of the complete graph on n vertices (with any number of colours) has a monochromatic subgraph isomorphic to S or a rainbow subgraph isomorphic to T. Here, a subgraph is said to be rainbow if all of its edges have different colours.
Po-Shen Loh, Benny Sudakov
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Computation of new diagonal graph Ramsey numbers
Electronic Journal of Graph Theory and Applications, 2022 For various connected simple graphs G, we extend the table of diagonal graph Ramsey numbers R(G, G) in ‘An Atlas of Graphs.’ This is accomplished by first converting the calculation of R(G, G) into a satisfiability problem in propositional logic ...
Richard M. Low +3 more
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