Abstract
Let G=(X,Y) be a 2-connected balanced bipartite graph with |X|=|Y|=n. In this paper, we prove that if |N(x 1)∪N(x 2)|+|N(y 1)∪N(y 2)|⩾n+2 for any {x 1,x 2}⊆X and {y 1,y 2}⊆Y , then G is hamiltonian except when G is a special graph on 8 or on 12 vertices.
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