An efficient condition for a graph to be Hamiltonian

Authors:
Shengjia Li;Ruijuan Li;Jinfeng Feng
Affiliations:
School of Mathematical Science, Shanxi University, 030006 Taiyuan, PR China;School of Mathematical Science, Shanxi University, 030006 Taiyuan, PR China;Lehrstuhl C für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 3
Cited 5

The Geng-Hua Fan conditions for pancyclic or Hamilton-connected graphs

Journal of Combinatorial Theory Series B
Updating the Hamiltonian problem—a survey

Journal of Graph Theory
Graph Theory With Applications

Graph Theory With Applications

A sufficient condition for pancyclic graphs

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

Theoretical Computer Science
Degree conditions on distance 2 vertices that imply k-ordered Hamiltonian

Discrete Applied Mathematics
On the 1-fault hamiltonicity for graphs satisfying Ore's theorem

Information Processing Letters
Disjoint cycles in hypercubes with prescribed vertices in each cycle

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

Let G=(V,E) be a 2-connected simple graph and let dG(u,v) denote the distance between two vertices u,v in G. In this paper, it is proved: if the inequality dG(u)+dG(v)≥| V(G)|-1 holds for each pair of vertices u and v with dG(u,v)=2, then G is Hamiltonian, unless G belongs to an exceptional class of graphs. The latter class is described in this paper. Our result implies the theorem of Ore [Note on Hamilton circuits, Amer. Math. Monthly 67 (1960) 55]. However, it is not included in the theorem of Fan [New sufficient conditions for cycles in graph, J. Combin. Theory Ser. B 37 (1984) 221-227].