Given i, j positive integers, let K denote a bipartite complete graph and let i, j ## Ε½ . R m, n be the smallest integer a such that for any r-coloring of the edges of K r a, a one can always find a monochromatic subgraph isomorphic to K . In other m, n Ε½ . Γ 4 words, if a G R m, n then every mat
On multicolor Ramsey numbers for complete bipartite graphs
β Scribed by Fan R.K Chung; R.L Graham
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 268 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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".
## Abstract Let __G__ be a simple undirected graph which has __p__ vertices and is rooted at __x__. Informally, the __rotation number h(G, x)__ of this rooted graph is the minimum number of edges in a __p__ vertex graph __H__ such that for each vertex __v__ of __H__, there exists a copy of __G__ in
It is shown that a graph of order N and average degree d that does not contain the book B m =K 1 +K 1, m as a subgraph has independence number at least Nf (d ), where f (x)t(log xΓx) (x Γ ). From this result we find that the book-complete graph Ramsey number satisfies r(B m , K n ) mn 2 Γlog(nΓe). I