Result: An efficient condition for a graph to be Hamiltonian

Title:
An efficient condition for a graph to be Hamiltonian
Source:
3rd Cologne/Twente Workshop on Graphs and Combinatorial OptimizationDiscrete applied mathematics. 155(14):1842-1845
Publisher Information:
Amsterdam; Lausanne; New York, NY: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 6 ref
Original Material:
INIST-CNRS
Document Type:
Conference Conference Paper
File Description:
text
Language:
English
Author Affiliations:
School of Mathematical Science, Shanxi University, 030006 Taiynan, China
Lehrstuhl C für Mathematik, RWTH Aachen University, 52056 Aachen, Germany
ISSN:
0166-218X
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Computer science; theoretical automation; systems

Mathematics
Accession Number:
edscal.19046566
Database:
PASCAL Archive

Further Information

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].