Given two graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G1 is a subgraph of G, or G2 is a subgraph of the complement of G. Let Pn denote a path of order n and K^m a kipas of order m + 1, i.e., the graph obtained from a Pm by adding one new vertex v and edges from v to all vertices of the Pm. We close the gap in existing knowledge on exact values of the Ramsey numbers R(Pn,K^m) by determining the exact values for the remaining open cases.
|Number of pages||8|
|Journal||Electronic journal of combinatorics|
|Publication status||Published - 14 Aug 2015|
- Ramsey number