An improved degree based condition for Hamiltonian cycles

Authors:
Lenin Mehedy;M. Kamrul Hasan;Mohammad Kaykobad
Affiliations:
Department of Computer Engineering, Kyung Hee University, 446-701, Republic of Korea;Department of Computer Engineering, Kyung Hee University, 446-701, Republic of Korea;Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology, Dhaka-1000, Bangladesh
Venue:
Information Processing Letters
Year:
2007

Citing 7
Cited 2

A lower bound on the number of Hamiltonian cycles

Discrete Mathematics
Computers and Intractability; A Guide to the Theory of NP-Completeness

Computers and Intractability; A Guide to the Theory of NP-Completeness
On Hamiltonian cycles and Hamiltonian paths

Information Processing Letters
A new sufficient condition for Hamiltonicity of graphs

Information Processing Letters
On k-ordered Hamiltonian graphs

Journal of Graph Theory
More than one tough chordal planar graphs are Hamiltonian

Journal of Graph Theory
Spanning 2-trails from degree sum conditions

Journal of Graph Theory

Note: A comprehensive analysis of degree based condition for Hamiltonian cycles

Theoretical Computer Science
On the 1-fault hamiltonicity for graphs satisfying Ore's theorem

Information Processing Letters

Quantified Score

Hi-index	0.89

Visualization

Abstract

A Hamiltonian cycle is a closed path through all the vertices of a graph. Since discovering whether a graph has a Hamiltonian path or a Hamiltonian cycle are both NP-complete problems, researchers concentrated on formulating sufficient conditions that ensure Hamiltonicity of a graph. A recent paper [M.S. Rahman, M. Kaykobad, On Hamiltonian cycles and Hamiltonian paths, Information Processing Letters 94 (2005) 37-41] presents distance based sufficient conditions for the existence of a Hamiltonian path. In this paper we establish that the same condition forces Hamiltonian cycle to be present excepting for the case where end points of a Hamiltonian path is at a distance of 2.