Estimating the circumference of a graph in terms of its leaf number

Abstract

Let T be the set of spanning trees of G and let L(T ) be the number of leaves in a tree T . The leaf number L(G) of G is defined as L(G) = max{L(T )|T ∈ T }. Let G be a connected graph of order n and minimum degree δ such that L(G) ≤ 2δ − 1.We show that the circumference of G is at least n − 1, and that if G is regular then G is hamiltonian.