New lower bounds for seven classical Ramsey numbers are obtained by considering some circulant graphs G n (A i ) with n β₯ 142 whose orders might be either prime or not. The results are
Lower bounds for multicolor classical Ramsey numbers
β Scribed by Wenlong Su; Haipeng Luo; Qiao Li
- Book ID
- 105643707
- Publisher
- SP Science China Press
- Year
- 1999
- Tongue
- English
- Weight
- 343 KB
- Volume
- 42
- Category
- Article
- ISSN
- 1674-7283
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π SIMILAR VOLUMES
## Abstract For any graph __G__, let __i__(__G__) and ΞΌ;(__G__) denote the smallest number of vertices in a maximal independent set and maximal clique, respectively. For positive integers __m__ and __n__, the lower Ramsey number __s__(__m, n__) is the largest integer __p__ so that every graph of or
The multicolor Ramsey number r k (C 4 ) is the smallest integer n for which any k-coloring of the edges of the complete graph K n must produce a monochromatic 4-cycle. It was proved earlier that r k (C 4 ) k 2 &k+2 for k&1 being a prime power. In this note we establish r k (C 4 ) k 2 +2 for k being