منابع مشابه
Ramsey goodness of paths
Article history: Received 19 December 2015 Available online 12 July 2016
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In a seminal paper from 1983, Burr and Erd1⁄2os started the systematic study of Ramsey numbers of cliques vs. large sparse graphs, raising a number of problems. In this paper we develop a new approach to such Ramsey problems using a mix of the Szemerédi regularity lemma, embedding of sparse graphs, Turán type stability, and other structural results. We give exact Ramsey numbers for various clas...
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Given a pair of graphs G and H, the Ramsey number R(G,H) is the smallest N such that every red-blue coloring of the edges of the complete graph KN contains a red copy of G or a blue copy of H. If a graph G is connected, it is well known and easy to show that R(G,H) ≥ (|G| − 1)(χ(H) − 1) + σ(H), where χ(H) is the chromatic number of H and σ(H) is the size of the smallest color class in a χ(H)-co...
متن کاملJozef Skokan Ramsey - goodness - and otherwise
A celebrated result of Chvátal, Rödl, Szemerédi and Trotter states (in slightly weakened form) that, for every natural number ∆, there is a constant r∆ such that, for any connected n-vertex graph G with maximum degree ∆, the Ramsey number R(G,G) is at most r∆n, provided n is sufficiently large. In 1987, Burr made a strong conjecture implying that one may take r∆ = ∆. However, Graham, Rödl and R...
متن کاملTripartite Ramsey numbers for paths
In this article, we study the tripartite Ramsey numbers of paths. We show that in any two-coloring of the edges of the complete tripartite graph K(n, n, n) there is a monochromatic path of length (1− o(1))2n. Since R(P2n+1,P2n+1) = 3n, this means that the length of the longest monochromatic path is about the same when two-colorings of K3n and K(n, n, n) are considered. © 2007 Wiley Periodicals,...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2017
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2016.06.009