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New lower bounds for seven classical Ramsey numbers

โœ Scribed by Kang Wu; Wenlong Su; Haipeng Luo; Xiaodong Xu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
346 KB
Volume
22
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

New lower bounds for seven classical Ramsey numbers are obtained by considering some circulant graphs G n (A i ) with n โ‰ฅ 142 whose orders might be either prime or not. The results are

๐Ÿ“œ SIMILAR VOLUMES

Lower bounds for lower Ramsey numbers
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## 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

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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