%0 Journal Article
%T Ramsey Numbers for Theta Graphs
%A M. M. M. Jaradat
%A M. S. A. Bataineh
%A S. M. E. Radaideh
%J International Journal of Combinatorics
%D 2011
%I Hindawi Publishing Corporation
%R 10.1155/2011/649687
%X The graph Ramsey number (1,2) is the smallest integer  with the property that any complete graph of at least  vertices whose edges are colored with two colors (say, red and blue) contains either a subgraph isomorphic to 1 all of whose edges are red or a subgraph isomorphic to 2 all of whose edges are blue. In this paper, we consider the Ramsey numbers for theta graphs. We determine (4,), (5,) for ¡Ý4. More specifically, we establish that (4,)=(5,)=2£¿1 for ¡Ý7. Furthermore, we determine (,) for ¡Ý5. In fact, we establish that (,)=(3/2)£¿1 if  is even, 2£¿1 if  is odd.
%U http://www.hindawi.com/journals/ijct/2011/649687/