Let G = Ka,b, where a, b are even or G = Ka,a -M 2a,, where a > 1 is an odd integer and M2a is a perfect matching in Ka,a. It has been shown ([3,4]) that G is arbitrarily decomposable into closed trails. Billington asked if the graph Kr,s, -F, where s,r are odd and F is a (smallest possible) spanning subgraph of odd degree, is arbitrarily decomposable into closed trails (). In this article we answer the question in the affirmative.
|Original language||English (US)|
|Number of pages||10|
|Journal||Journal of Combinatorial Mathematics and Combinatorial Computing|
|State||Published - Aug 1 2010|