文摘
Let \(G_1\) and \(G_2\) be two given graphs. The Ramsey number \(R(G_1,G_2)\) is the least integer r such that for every graph G on r vertices, either G contains a \(G_1\) or \(\overline{G}\) contains a \(G_2\). A complete bipartite graph \(K_{1,n}\) is called a star. The kipas \(\widehat{K}_n\) 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.