Hamiltonicity, minimum degree and leaf number

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

“…After that, Mukwembi [15] proved that if G is a connected claw-free graph with δ(G) ≥ (L(G) + 1)/2, then G is hamiltonian. In recent years, several authors reported on sufficient conditions for a graph to be hamiltonian or traceable based on minimum degree and leaf number, see [9][10][11][12][13].…”

“…Theorem 1. [12] If G is a connected graph with δ(G) ≥ (L(G)+2)/2, then G is hamiltonian. Let p(G) and c(G) be the order of a longest path and a longest cycle in a graph G, respectively.…”