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Multipartite Graph-Tree Ramsey Numbers

✍ Scribed by PAUL ERDÖS; R. J. FAUDREE; C. C. ROUSSEAU; R. H. SCHELP

Book ID
119862761
Publisher
John Wiley and Sons
Year
1989
Tongue
English
Weight
449 KB
Volume
576
Category
Article
ISSN
0890-6564

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📜 SIMILAR VOLUMES

Tree-complete graph ramsey numbers
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✍ V. Chvátal 📂 Article 📅 1977 🏛 John Wiley and Sons 🌐 English ⚖ 50 KB

## Abstract The ramsey number of any tree of order __m__ and the complete graph of order __n__ is 1 + (__m__ − 1)(__n__ − 1).

On Ramsey numbers involving starlike mul
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The Ramsey number r ( G , H ) is evaluated exactly in certain cases in which both G and H are complete multipartite graphs K(n,, n2, ..., n k ) . Specifically, each of the following cases is handled whenever n is sufficiently large: r(K(1, m,, ..., m k ) , K(1, n)), r(K(1, m), K(n,, ..., nk, n)), pr

Small order graph-tree Ramsey numbers
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With but a few exceptions, the Ramsey number r(G, T) is determined for all connected graphs G with at most five vertices and all trees T.

Extremal theory and bipartite graph-tree
Extremal theory and bipartite graph-tree Ramsey numbers
✍ P. Erd'́os; R.J. Faudree; C.C. Rousseau; R.H. Schelp 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 675 KB

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

Multipartite Ramsey numbers for odd cycl
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✍ András Gyárfás; Gábor N. Sárközy; Richard H. Schelp 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 119 KB

## Abstract In this paper we study multipartite Ramsey numbers for odd cycles. We formulate the following conjecture: Let __n__≥5 be an arbitrary positive odd integer; then, in any two‐coloring of the edges of the complete 5‐partite graph __K__((__n__−1)/2, (__n__−1)/2, (__n__−1)/2, (__n__−1)/2, 1)