On Hamiltonian cycles and Hamiltonian paths

Authors:
M. Sohel Rahman;M. Kaykobad
Affiliations:
Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh;Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh and Department of Computer Science and Engineering, North South Universi ...
Venue:
Information Processing Letters
Year:
2005

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Abstract

A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore's theorem directly follows from our result.