Monochromatic coverings and tree Ramsey numbers
نویسندگان
چکیده
منابع مشابه
Monochromatic tree covers and Ramsey numbers for set-coloured graphs
We extend results on monochromatic tree covers and from classical Ramsey theory to a generalised setting, where each of the edges of an underlying host graph (here, either a complete graph or a complete bipartite graph), is coloured with a set of colours. Our results for tree covers in this setting have an application to Ryser’s Conjecture. Every r-partite r-uniform hypergraph whose edges pairw...
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We denote by r'( G I , G2 ) the ramsey number of two graphs and G2 • If Tp+l is a tree of order p + 1 which is not a star, and if jJ is not a divisor of the positive integer q 1, then we shall show that r(Tp+b ](l,q) ::; p + q 1, and we shall describe some trees and stars for which equality holds. Furthermore. we detf'rmine the ramsey numbers r(T;+l' Tq*+l) for p, q ~ 4, where T~ denotes a tree...
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The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...
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The typical problem in (generalized) Ramsey theory is to find the order of the largest monochromatic member of a family F (for example matchings, paths, cycles, connected subgraphs) that must be present in any edge coloring of a complete graph Kn with t colors. Another area is to find the minimum number of monochromatic members of F that partition or cover the vertex set of every edge colored c...
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For a positive integer n and graph B, fa (n) is the least integer m such that any graph of order n and minimal degree m has a copy of B. It will be show that if B is a bipartite graph with parts of order k and i (k-1), then there exists a positive constant c, such that for any tree T of order n and for any j (0-j _-(k-1)), the Ramsey number r(T, B) < n + c-(fe (n)) 't(k-1) if A(T)-(n/(k-j-1))-(...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90179-1