Results 11 to 20 of about 9,500 (263)
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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Ramsey Numbers for Connected 2-Colorings of Complete Graphs
Theory and Applications of Graphs, 2023 In 1978, David Sumner introduced a variation of Ramsey numbers by restricting to 2-colorings in which the subgraphs spanned by edges in each color are connected.
Mark Budden
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Journal of Combinatorial Theory, Series B, 1993 The planar Ramsey number \(\text{PR}(k,\ell)\) \((k,\ell\geq 2)\) is the smallest integer \(n\) such that any planar graph on \(n\) vertices contains either a complete graph on \(k\) vertices or an independent set of size \(\ell\). We find exact values of \(\text{PR}(k,\ell)\) for all \(k\) and \(\ell\).
Richard Steinberg, Craig A. Tovey
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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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A note on the Ramsey numbers for theta graphs versus the wheel of order 5
AKCE International Journal of Graphs and Combinatorics, 2018 The study of exact values and bounds on the Ramsey numbers of graphs forms an important family of problems in the extremal graph theory. For a set of graphs S and a graph F , the Ramsey number R (S , F) is the smallest positive integer r such that for ...
Mohammed M.M. Jaradat +3 more
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Discrete Mathematics, 1996 For a graph-theoretic parameter \(f\), an integer \(m\) and a graph \(H\), the mixed Ramsey number \(v(f;m;H)\) is the least positive integer \(p\) such that if \(G\) is any graph of order \(p\), then either \(f(G) \geq m\) or \(\overline G\) contains a subgraph isomorphic to \(H\).
Nirmala Achuthan +2 more
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Tower Gaps in Multicolour Ramsey Numbers
Forum of Mathematics, Sigma, 2023 Resolving a problem of Conlon, Fox and Rödl, we construct a family of hypergraphs with arbitrarily large tower height separation between their $2$ -colour and q-colour Ramsey numbers.
Quentin Dubroff +3 more
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On Ramsey numbers of hedgehogs [PDF]
Combinatorics, Probability and Computing, 2019 AbstractThe hedgehog Ht is a 3-uniform hypergraph on vertices $1, \ldots ,t + \left({\matrix{t \cr 2}}\right)$ such that, for any pair (i, j) with 1 ≤ i < j ≤ t, there exists a unique vertex k > t such that {i, j, k} is an edge. Conlon, Fox and Rödl proved that the two-colour Ramsey number of the hedgehog grows polynomially in the number of its ...
Jacob Fox, Ray Li
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A General Lower Bound on Gallai-Ramsey Numbers for Non-Bipartite Graphs
Theory and Applications of Graphs, 2018 Given a graph $H$ and a positive integer $k$, the $k$-color Gallai-Ramsey number $gr_{k}(K_{3} : H)$ is defined to be the minimum number of vertices $n$ for which any $k$-coloring of the complete graph $K_{n}$ contains either a rainbow triangle or a ...
Colton Magnant
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