Three color Ramsey number of K4 − e

✍ Scribed by Geoffrey Exoo

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 300 KB
• Volume: 89
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90122-i

✦ Synopsis

Exoo, G., Three color Ramsey number of K, -e, Discrete Mathematics 89 (1991) 301-305.

We show that 28 s r(K4 -e; 3) G 32. The construction used to establish the lower bound is made by using the strongly regular Schllfli graph for one of the colors, and then by partitioning its complement into two isomorphic graphs. The coloring has the property that each edge is on exactly one monochromatic K,, hence the vertex sets of these K,'s form a Steiner triple system.