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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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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.
Loh, Po-Shen, Sudakov, Benny
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A class of Ramsey-extremal hypergraphs [PDF]
Transactions on Combinatorics, 2017 In 1991, McKay and Radziszowski proved that, however each $3$-subset of a $13$-set is assigned one of two colours, there is some $4$-subset whose four $3$-subsets have the same colour. More than 25 years later, this remains the only non-trivial
Brendan D. McKay
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A Note on On-Line Ramsey Numbers for Some Paths
Mathematics, 2021 We consider the important generalisation of Ramsey numbers, namely on-line Ramsey numbers. It is easiest to understand them by considering a game between two players, a Builder and Painter, on an infinite set of vertices. In each round, the Builder joins
Tomasz Dzido, Renata Zakrzewska
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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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Anti-Ramsey Hypergraph Numbers [PDF]
Electronic Journal of Graph Theory and Applications, 2021 Summary: The anti-Ramsey number \(ar_n(H)\) 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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AKCE International Journal of Graphs and Combinatorics, 2020 A sequence of graphs is a Ramsey sequence if for every positive integer k, the graph Gk is isomorphic to a proper subgraph of and for each positive integer k, there is an integer such that every red-blue coloring of Gn results in a monochromatic Gk. Some
Gary Chartrand, Ping Zhang
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Cycle-Complete Ramsey Numbers [PDF]
International Mathematics Research Notices, 2019 Abstract The Ramsey number $r(C_{\ell },K_n)$ is the smallest natural number $N$ such that every red/blue edge colouring of a clique of order $N$ contains a red cycle of length $\ell $ or a blue clique of order $n$. In 1978, Erd̋s, Faudree, Rousseau, and Schelp conjectured that $r(C_{\ell },K_n) = (\ell -1)(n-1)+1$ for $\ell \geq n\geq 3$
Keevash, Peter +2 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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Star-critical connected Ramsey numbers for 2-colorings of complete graphs [PDF]
Transactions on CombinatoricsThis paper builds upon Sumner's work by further investigating the concept of connected Ramsey numbers, specifically focusing on star-critical connected Ramsey numbers.
Monu Moun, Jagjeet Jakhar, Mark Budden
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