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IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2022 We initiate the study of Ramsey numbers of trails. Let $k \geq 2$ be a positive integer. The Ramsey number of trails with $k$ vertices is defined as the the smallest number $n$ such that for every graph $H$ with $n$ vertices, $H$ or the complete $\overline{H}$ contains a trail with $k$ vertices.
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One More Turán Number and Ramsey Number for the Loose 3-Uniform Path of Length Three
Discussiones Mathematicae Graph Theory, 2017 Let P denote a 3-uniform hypergraph consisting of 7 vertices a, b, c, d, e, f, g and 3 edges {a, b, c}, {c, d, e}, and {e, f, g}. It is known that the r-color Ramsey number for P is R(P; r) = r + 6 for r ≤ 9.
Polcyn Joanna
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On-line Ramsey numbers for paths and stars [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Graphs and ...
J. A. Grytczuk +2 more
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Ramsey numbers of cycles versus general graphs
Forum of Mathematics, Sigma, 2023 The Ramsey number $R(F,H)$ is the minimum number N such that any N-vertex graph either contains a copy of F or its complement contains H. Burr in 1981 proved a pleasingly general result that, for any graph H, provided n is sufficiently large, a ...
John Haslegrave +3 more
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Ramsey numbers for tournaments
Theoretical Computer Science, 2001 Let \(D_1,\dots, D_k\) be acyclic digraphs (possibly several are isomorphic). The authors define the \(k\)-color Ramsey number \(r(D_1,\dots, D_k)\) as the largest integer \(r\) for which there exists a tournament \(T= (V,A)\) on \(r\) vertices and a \(k\)-coloring \(\phi: A\to \{1,\dots, k\}\) of its arc set such that no \(D_i\) is a subdigraph of \(T\
Yannis Manoussakis, Zsolt Tuza
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On a Variation of the Ramsey Number [PDF]
Transactions of the American Mathematical Society, 1972 Let c ( m , n ...
Chartrand, Gary, Schuster, Seymour
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Generalization of Ramsey Number for Cycle with Pendant Edges
MathematicsThis paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number.
Jagjeet Jakhar +5 more
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On size multipartite Ramsey numbers for stars versus paths and cycles
Electronic Journal of Graph Theory and Applications, 2017 Let $K_{l\times t}$ be a complete, balanced, multipartite graph consisting of $l$ partite sets and $t$ vertices in each partite set. For given two graphs $G_1$ and $G_2$, and integer $j\geq 2$, the size multipartite Ramsey number $m_j(G_1,G_2)$ is the ...
Anie Lusiani +2 more
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European Journal of Combinatorics, 1982 In the first section of this paper it is shown that the bipartite Ramsey number br(m, n) satisfies br(m, n)⩽2m(n−1)+1. (Beineke and Schwenk [1] conjectured br(m, n) = 2m(n−1) + 1 but Irving [17] showed that equality does not always hold.) The second section gives a conjecture for the Ramsey numbers of the complete graphs, and lastly the numbers of ...
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