Abstract
We show that, in any colouring of the edges of K_53 with two colours, there exists a monochromatic K_5, and hence R(5,5) <= 53. This is accomplished in three stages: a full enumeration of edges in (4,5)-good graphs, and a proof of the nonexistence of (5,5)-good graphs on 53 vertices. Only the first stage required extensive help from the computer.
Publication Date
1992
Document Type
Article
Department, Program, or Center
Center for Advancing the Study of CyberInfrastructure
Recommended Citation
Australasian Journal of Combinatorics 5 (1992) 13-20
Campus
RIT – Main Campus
COinS
Comments
This article is also available at the publisher's website at: http://ajc.maths.uq.edu.au/ ISSN:1034-4942 Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.