For bipartite graphs G1,G2 ..... Gk, the bipartite Ramsey number b(GI,G2,...,Gk) is the least positive integer b so that any colouring of the edges of Kb, b with k colours will result in a copy of Gi in the ith colour for some i. In this note, we establish the exact value of the bipartite Ramsey num
A bipartite Ramsey number
β Scribed by Geoffrey Exoo
- Publisher
- Springer Japan
- Year
- 1991
- Tongue
- English
- Weight
- 101 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0911-0119
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## Abstract We determine the maximum number of colors in a coloring of the edges of __K~m,n~__ such that every cycle of length 2__k__ contains at least two edges of the same color. One of our main tools is a result on generalized path covers in balanced bipartite graphs. For positive integers __q__
Erd6s. P. and C.C. Rousseau, The size Ramsey number of a complete bipartite graph, Discrete Mathematics 113 (1993) 259-262. In this note we prove that the (diagonal) size Ramsey number of K,,.,, is bounded below by $2'2".
For a positive integer n and graph E, fs(n) is the least integer m such that any graph of order n and minimal degree m has a copy of B. It will be show that if B is a bipartite graph with parts of order k and 1 (k G I), then there exists a positive constant c, such that for any tree T,, of order II