Ramsey numbers of trees and unicyclic graphs versus fans

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Ramsey numbers of trees versus fans

For two given graphsG1 andG2, the RamseynumberR(G1,G2) is the smallest integerN such that, for any graph G of order N , either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. Let Tn be a tree of order n, Sn a star of order n, and Fm a fan of order 2m + 1, i.e., m triangles sharing exactly one vertex. In this paper, we prove that R(Tn, Fm) = 2n − 1 for n ≥ 3m2 − 2m ...

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2017

ISSN: 0012-365X

DOI: 10.1016/j.disc.2016.12.020