On Double-Star Decomposition of Graphs

A tree containing exactly two non-pendant vertices is called a double-star. A double-star with degree sequence ( + 1, + 1, 1, . . . , 1) is denoted by . We study the edge-decomposition of graphs into double-stars. It was proved that every double-star of size decomposes every 2 -regular graph. In this paper, we extend this result by showing that every graph in which every vertex has degree 2 + 1 or 2 + 2 and containing a 2-factor is decomposed into and , for all positive integers and such that + =