Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2008-12-06

Journal: DISCRETE MATHEMATICS

Included Journals: Scopus、EI、SCIE

Volume: 308

Issue: 23

Page Number: 5841-5848

ISSN: 0012-365X

Key Words: Planar graph; Ramsey number; Forbidden subgraph; Cycle

Abstract: The planar Ramsey number PR(H-1, H-2) is the smallest integer it Such that any planar graph on it vertices contains a copy of H-1 or its complement contains a copy of H-2. It is known that the Ramsey number R(C-4, K-7) = 22. The planar Ramsey numbers PR(C-4, K-1) for l <= 6 are known. In this paper we show that PR(C-4, K-7) = 20. (C) 2008 Published by Elsevier B.V.