Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

In this paper we study three-color Ramsey numbers. Let K i,j denote a complete i by jbipartite graph. We shall show that (i) for any connected graphs G 1, G 2 and G 3, if r(G 1,G 2)≥s(G 3), then r(G 1, G 2, G 3)≥(r(G 1, G 2)−1)(χ(G 3)−1)+s(G 3), where s(G 3) is the chromatic surplus of G 3; (ii) (k+m−2)(n−1)+1≤r(K 1,k , K 1,m , K n )≤ (k+m−1)(n−1)+1, and ifk or m is odd, the second inequality becomes an equality; (iii) for any fixed mk≥2, there is a constant c such that r(K k,m , K k,m , K n )≤c(n/logn), and r(C 2m , C 2m , K n )≤c(n/logn) m/(m−1) for sufficiently large n.

Keywords

Monochromatic graph, Three-color Ramsey number

Publication Date

2003

Source Publication Title

Graphs and Combinatorics

Volume

19

Issue

2

Start Page

249

End Page

258

Publisher

Springer Verlag

Peer Reviewed

1

DOI

10.1007/s00373-002-0495-7

Link to Publisher's Edition

http://dx.doi.org/10.1007/s00373-002-0495-7

ISSN (print)

14355914

Included in

Mathematics Commons

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