Degree bounded forest covering

Abstract

We prove that for an undirected graph with arboricity at most k+∈, its edges can be decomposed into k forests and a subgraph with maximum degree [k∈+1/1-∈]. The problem is solved by a linear programming based approach: we first prove that there exists a fractional solution to the problem, and then use a result on the degree bounded matroid problem by Király, Lau and Singh [5] to get an integral solution. © 2011 Springer-Verlag.