Sciweavers

Share
GC
2011
Springer

Ramsey Numbers of Some Bipartite Graphs Versus Complete Graphs

8 years 9 months ago
Ramsey Numbers of Some Bipartite Graphs Versus Complete Graphs
The Ramsey number r(H, Kn) is the smallest positive integer N such that every graph of order N contains either a copy of H or an independent set of size n. The Tur´an number ex(m, H) is the maximum number of edges in a graph of order m not containing a copy of H. We prove the following two results: (1) Let H be a graph obtained from a tree F of order t by adding a new vertex w and joining w to each vertex of F by a path of length k such that any two of these paths share only w. Then r(H, Kn) ≤ ck,t n1+1/k ln1/k n , where ck,t is a constant depending only on k and t. This generalizes some results in [11], [13], and [16]. (2) Let H be a bipartite graph with ex(m, H) = O(mγ), where 1 < γ < 2. Then r(H, Kn) ≤ cH n ln n 1/(2−γ) , where cH is a constant depending only on H. This generalizes a result in [4]. Key words. Ramsey number, independence number
Tao Jiang, Michael Salerno
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where GC
Authors Tao Jiang, Michael Salerno
Comments (0)
books