A generalization of fan's condition and forbidden subgraph conditions for hamiltonicity

Abstract

Let G be a 2-connected graph with n vertices and H be an induced subgraph of G. Denote V₀ ≔ {v ϵ V(G): d(v) ⩾ n/2}. If there exists a pair of vertices x and y at distance 2 in H such that {x, y} ⊆ V(H)βV₀, then H is called degree light. Let F be the unique graph with degree sequence (1, 1, 1, 3, 3, 3). In this paper, we prove that if G contains no degree light K_{1, 3} and every degree light F of G contains no induced P₄ of G − V₀, then G is hamiltonian.