New Upper Bounds for Ramsey Numbers
โ Scribed by Y.R Huang; K.M Zhang
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 79 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
โฆ Synopsis
The Ramsey number R(G 1 , G 2 ) is the smallest integer p such that for any graph
Some new upper bound formulas are obtained for R(G 1 , G 2 ) and R(m, n), and we derive some new upper bounds for Ramsey numbers here.
๐ SIMILAR VOLUMES
New upper bounds for the ramsey numbers r ( k , I ) are obtained. In particular it is shown there is a constant A such that The ramsey number r(k, l ) is the smallest integer n, such that any coloring with red and blue of the edges of the complete graph K , of order n yields either a red K , subgra
In this paper we show that for n โฅ 4, R(3, 3, . . . , 3) < n!( e-e -1 + 3 2 ) + 1. Consequently, a new bound for Schur numbers is also given. Also, for even n โฅ 6, the Schur number S n is bounded by S n < n!( e-e -1 + 3 2 ) -n + 2.
## 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
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
## dedicated to the memory of rodica simion Let G be an r-uniform hypergraph. The multicolor Ramsey number r k G is the minimum n such that every k-coloring of the edges of the complete r-uniform hypergraph K r n yields a monochromatic copy of G. Improving slightly upon results from M. Axenovich,