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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 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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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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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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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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Integers, 2016 The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about triangular sets are proved. This game is easy enough that young children are able to play. The most basic variations of
Zachary Chaney +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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