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 if n is odd. We use methods similar to those used for isomorphic factorizations of complete graphs into spanning trees. In of this article, we show that our methods do not work for isomorphic factorizations of into tadpoles if n is even.

Keywords

• factorization
• complete graphs
• unicyclic graphs
• tadpoles