Ramsey goodness and generalized stars
نویسندگان
چکیده
منابع مشابه
Ramsey goodness and beyond
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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Article history: Received 19 December 2015 Available online 12 July 2016
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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...
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The double star S(n, m), where n * m a 0, is the graph cons isting of the union of two stars &I and &n together with a line joining their centers. Its rsmsey number r(S(n, m)) is the least number p such that there is a monochromatic copy of S(n, m) in any 2-coloring of the edges of Kpa It is shown that r(S(n, m)) = max (2n + 1, n + 2m + 2) if n is odd and m G 2; and r(S(n, m)) = max (2n + 2, n ...
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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...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2010
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2009.10.011