Ramsey goodness and beyond
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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ژورنال
عنوان ژورنال: Combinatorica
سال: 2009
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-009-2409-2