Hamiltonicity of bipartite biclaw-free graphs

AbstractWe define a simple bipartite graph to be biclaw-free if it contains no induced subgraph isomorphic to H, where H can be obtained from two copies of K1, 3 by adding an edge between the two vertices of degree 3. We show that every connected bipartite biclaw-free graph with minimum degree δ⩾6 has connectivity at least δ−2 and that every connected balanced bipartite biclaw-free graph with minimum degree δ⩾9 and order n⩽6δ− 14 is hamiltonian