On 2-Connected Spanning Subgraphs with Bounded Degree in K 1,r -Free Graphs

Abstract

For any integer r > 1, an r-trestle of a graph G is a 2-connected spanning subgraph F with maximum degree Δ(F) ≤ r. A graph G is called K 1,r -free if G has no K 1,r as an induced subgraph. Inspired by the work of Ryjacek and Tkac, we show that every 2-connected K 1,r -free graph has an r-trestle. The paper concludes with a corollary of this result for the existence of k-walks.