There is a family (H k ) of graphs such that H k has order (1+o(1))(-2รe) k 2 kร2 but has no clique or stable set of order k. This result of Spencer provides the best known lower bound for the diagonal Ramsey numbers R(k, k). Here we see that the graphs H k can be taken to be regular, self-complemen
Lower bounds for small diagonal ramsey numbers
โ Scribed by James B Shearer
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 129 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0097-3165
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A new construction of self-complementary graphs containing no Klo or K , is described. This construction gives the Ramsey number lower bounds r(10,lO) 2 458 and r(1 1,l 1 ) 2 542. The problem of determining the Ramsey numbers is known to be very difficult and so we are often satisfied with partial
## Abstract For any graph __G__, let __i__(__G__) and ฮผ;(__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