Results 21 to 30 of about 21,406 (168)
A note on the size Ramsey numbers for matchings versus cycles [PDF]
Mathematica Bohemica, 2021 For graphs $G$, $F_1$, $F_2$, we write $G \rightarrow(F_1, F_2)$ if for every red-blue colouring of the edge set of $G$ we have a red copy of $F_1$ or a blue copy of $F_2$ in $G$.
Edy Tri Baskoro, Tomáš Vetrík
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Generalized Ramsey numbers for paths in 2-chromatic graphs
International Journal of Mathematics and Mathematical Sciences, 1986 Chung and Liu have defined the d-chromatic Ramsey number as follows. Let 1≤d≤c and let t=(cd). Let 1,2,…,t be the ordered subsets of d colors chosen from c distinct colors. Let G1,G2,…,Gt be graphs. The d-chromatic Ramsey number denoted by rdc(G1,G2,…,Gt)
R. Meenakshi, P. S. Sundararaghavan
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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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Restricted size Ramsey number for path of order three versus graph of order five
Electronic Journal of Graph Theory and Applications, 2017 Let $G$ and $H$ be simple graphs. The Ramsey number for a pair of graph $G$ and $H$ is the smallest number $r$ such that any red-blue coloring of edges of $K_r$ contains a red subgraph $G$ or a blue subgraph $H$.
Denny Riama Silaban +2 more
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Star-Critical Ramsey Numbers for Cycles Versus K4
Discussiones Mathematicae Graph Theory, 2021 Given three graphs G, H and K we write K → (G, H), if in any red/blue coloring of the edges of K there exists a red copy of G or a blue copy of H. The Ramsey number r(G, H) is defined as the smallest natural number n such that Kn → (G, H) and the star ...
Jayawardene Chula J. +2 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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