Results 61 to 70 of about 21,406 (168)
Discrete Mathematics, 1999 In classical Ramsey literature usually Ramsey numbers for complete graphs are studied, and it is asked how large they can be. Since Ramsey numbers are monotone functions in the edges of the excluded graphs, one can also investigate the other end, and ask how small a nontrivial Ramsey number of a graph on \(n\) vertices can be.
Csákány, Rita, Komlós, János
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The k-Ramsey number of two five cycles
AKCE International Journal of Graphs and CombinatoricsGiven any two graphs F and H, the Ramsey number R(F, H) is defined as the smallest positive integer n such that every red-blue coloring of the edges of the complete graph Kn of order n, there will be a subgraph of Kn isomorphic to F whose edges are all ...
Johannes H. Hattingh +2 more
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Discrete Applied Mathematics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heiko Harborth, Meinhard Möller
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On Ramsey numbers for trees versus fans of even order
Indonesian Journal of CombinatoricsGiven two graphs G and H. The graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or F̅ contains a copy of H.
Intan Sherlin +3 more
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On a generalization of Ramsey numbers
Discrete Mathematics, 1973 Define \(m=N(l_1,k_1;l_2,k_2;r)\) as the smallest integer with the property that if the \(r\)-tuples of a set of \(m\) elements are arbitrarily split into two classes then for \(i=1\) or \(2\) there exists a subset of size \(l_i\) each of whose subsets of size \(k_i\) lies in some \(r\)-subset of the \(i\)-th class.
Paul Erdös, Patrik E. O'Neil
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A Note on Upper Bounds for Some Generalized Folkman Numbers
Discussiones Mathematicae Graph Theory, 2019 We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special cases of generalized edge Folkman numbers, including the cases Fe(K3, K4 − e; K5) ≤ 27 and Fe(K4 −
Xu Xiaodong +2 more
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Discrete Mathematics, 2002 Let \(f_1\) and \(f_2\) be graphical parameters of positive integers. Let \(m\) and \(n\) be positive integers. Define the Ramsey number \(r(f_1\geq m\); \(f_2\geq n\)) as the least positive integer \(N\) such that for any graph \(G\) of order \(N\) either \(f_1(G)\geq m\) or \(f_2(\overline G)\geq n\).
Wai Chee Shiu +2 more
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Journal of Combinatorial Theory, Series A, 1980 AbstractUpper bounds are found for the Ramsey function. We prove R(3, x) < cx2lnx and, for each k ⩾ 3, R(k, x) < ckxk − 1(ln x)k − 2 asymptotically in x.
Miklós Ajtai +2 more
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, 2018 The Ramsey number \(R_X(p,q)\) for a class of graphs X is the minimum n such that every graph in X with at least n vertices has either a clique of size p or an independent set of size q. We say that Ramsey number is linear in X if there is a constant k such that \(R_{X}(p,q) \le k(p+q)\) for all p, q.
Aistis Atminas +2 more
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On Monochromatic Subgraphs of Edge-Colored Complete Graphs
Discussiones Mathematicae Graph Theory, 2014 In a red-blue coloring of a nonempty graph, every edge is colored red or blue. If the resulting edge-colored graph contains a nonempty subgraph G without isolated vertices every edge of which is colored the same, then G is said to be monochromatic.
Andrews Eric +4 more
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