Rainbow matchings in edge-colored complete split graphs

Abstract

In 1973, Erdős et al. introduced the anti-Ramsey number for a graph G in Kn, which is defined to be the maximum number of colors in an edge-coloring of Kn which does not contain any rainbow G. This is always regarded as one of rainbow generalizations of the classic Ramsey theory. Since then the anti-Ramsey numbers for several special graph classes in complete graphs have been determined. Also, the researchers generalized the host graph for the anti-Ramsey number from the complete graph to general graphs, including bipartite graphs, complete split graphs, planar graphs, and so on. In this paper, we study the anti-Ramsey number of matchings in the complete split graph. Since the complete split graph contains the complete graph as a subclass, the results in this paper cover the previous results about the anti-Ramsey number of matchings in the complete graph.