| Abstract: | A graph G is co-connected if both G and its complement ? are connected and nontrivial. For two graphs A and B, the connected Ramsey number rc(A, B) is the smallest integer n such that there exists a co-connected graph of order n, and if G is a co-connected graph on at least n vertices, then A ? G or B ? ?. If neither A or B contains a bridge, then it is known that rc(A, B) = r(A, B), where r(A, B) denotes the usual Ramsey number of A and B. In this paper rc(A, B) is calculated for some pairs (A, B) when r(A, B) is known and at least one of the graphs A or B has a bridge. In particular, rc(A, B) is calculated for A a path and B either a cycle, star, or complete graph, and for A a star and B a complete graph. |
