Factorizations of complete graphs into tadpoles

Abstract

A tadpole (also a canoe paddle or lollipop) is a graph that arises from a cycle and a path by gluing a terminal vertex of the path to an arbitrary vertex of the cycle. In this article, we show that all tadpoles factorize the complete graph K2n+1 if n is odd. We use methods similar to those used for isomorphic factorizations of complete graphs K2n into spanning trees. In Section 4 of this article, we show that our methods do not work for isomorphic factorizations of K2n+1 into tadpoles if n is even.