The hamiltonicity of bipartite graphs involving neighborhood unions

Abstract

AbstractLet G=(X,Y) be a 2-connected balanced bipartite graph with |X|=|Y|=n. In this paper, we prove that if |N(x1)∪N(x2)|+|N(y1)∪N(y2)|⩾n+2 for any {x1,x2}⊆X and {y1,y2}⊆Y, then G is hamiltonian except when G is a special graph on 8 or on 12 vertices