Let G1 and G2 be two given graphs. The Ramsey number R(G1,G2) is the least integer r such that for every graph G on r vertices, either G contains a G1 or the complement of G contains a G2. A complete bipartite graph K1,n is called a star. The kipas of order n+1 is the graph obtained from a path of order n by adding a new vertex and joining it to all the vertices of the path. Alternatively, a kipas is a wheel with one edge on the rim deleted. Whereas for star-wheel Ramsey numbers not all exact values are known to date, in contrast we determine all exact values of star-kipas Ramsey numbers.
- Ramsey number