Abstract
A graph G is called { H 1 , H 2 , … , H k } -free if G contains no induced subgraph isomorphic to any H i , 1 ⩽ i ⩽ k . Let G be a 2-connected { K 1 , 4 , K 1 , 4 + e } -free graph of order n ⩾ 13 . If δ ( G ) ⩾ n / 4 , then G is hamiltonian or G ∈ F , where K 1 , 4 + e is a graph obtained by joining a pair of nonadjacent vertices in a K 1 , 4 and F is a family of nonhamiltonian graphs of connectivity 2.
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