Result: An efficient condition for a graph to be Hamiltonian
Title:
An efficient condition for a graph to be Hamiltonian
Authors:
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
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Théorie des graphes, Graph theory, Sciences appliquees, Applied sciences, Informatique; automatique theorique; systemes, Computer science; control theory; systems, Informatique théorique, Theoretical computing, Algorithmique. Calculabilité. Arithmétique ordinateur, Algorithmics. Computability. Computer arithmetics, Recherche information. Graphe, Information retrieval. Graph, Circuit, Circuito, Combinatoire, Combinatorics, Combinatoria, Condition suffisante, Sufficient condition, Condición suficiente, Cycle graphe, Cycle(graph), Ciclo diagrama, Cycle hamiltonien, Hamiltonian cycle, Ciclo hamiltoniano, Distance, Distancia, Graphe connexe, Connected graph, Grafo conexo, Graphe hamiltonien, Hamiltonian graph, Grafo hamiltoniano, Hamiltonien, Hamiltonian, Hamiltoniano, Informatique théorique, Computer theory, Informática teórica, Optimisation, Optimization, Optimización, 05C45, 68R10, Graphe simple, 05C12; 05C45, Distance; Hamiltonian cycle; Sufficient condition
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
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
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
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].