Construction Schemes of Hamiltonian Laceable and Bipancyclic Graphs

Abstract

In this paper, we study some hamiltonian properties of bipartite graphs. Every hamiltonian bipartite graph G = (V0 ∪ V1,E) satisfies |V0| = |V1|. Since the colors of a path in bipartite graphs alternate, any hamiltonian bipartite graphs cannot be hamiltonian connected. Thus, the concepts of hamiltonian laceability, strongly hamiltonian laceability, hyper-hamiltonian laceability, bipancyclicity, and edge-bipancyclicity for hamiltonian bipartite graphs are attractive topics in interconnection networks. In this paper, we propose several methods, which extend the result in [7], to construct hamiltonian laceable, strongly hamiltonian laceable, and hyper-hamiltonian laceable graphs. We also show that our construction schemes preserve bipancyclic and edge-bipancyclic properties.