Lower bounds on the leaf number in graphs with forbidden subgraphs

Abstract

Let G be a simple, connected graph. The leaf number, L(G) of G, is defined as the maximum number of leaf vertices contained in a spanning tree of G. Assume that G is a triangle−free graph with minimum degree δ, order n and leaf number L(G). We show that for δ = 4 and δ = 5, where cδ is a constant that depends on δ only. Similar bounds are shown to hold for triangle−free and C4−free graphs.