Covering cycles in sparse graphs

Abstract

AbstractLet be an integer. Kouider and Lonc proved that the vertex set of every graph G with vertices and minimum degree at least can be covered by cycles. Our main result states that for every and , the same conclusion holds for graphs G with minimum degree that are sparse in the sense that In particular, this allows us to determine the local resilience of random and pseudorandom graphs with respect to having a vertex cover by a fixed number of cycles. The proof uses a version of the absorbing method in sparse expander graphs.