Improved Sufficient Conditions for Hamiltonian Properties

• Autorzy: Jens-P. Bode , Anika Fricke , Arnfried Kemnitz
• Języki publikacji: EN

Abstrakty

EN

In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity condition.

Słowa kluczowe

EN

Hamiltonian; traceable; Hamiltonian-connected

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 2
• Strony: 329-334

Daty

wydano

2015-05-01

otrzymano

2014-01-20

poprawiono

2014-09-03

zaakceptowano

2014-09-03

online

2015-04-18

Twórcy

autor

Jens-P. Bode

• Computational Mathematics Technische Universität Braunschweig 38092 Braunschweig, Germany

autor

Anika Fricke

• Zentrum für erfolgreiches Lehren und Lernen Ostfalia Hochschule für angewandte Wissenschaften 38302 Wolfenbüttel, Germany

autor

Arnfried Kemnitz

• Computational Mathematics Technische Universität Braunschweig 38092 Braunschweig, Germany

Bibliografia

• [1] J.-P. Bode, A. Kemnitz, I. Schiermeyer and A. Schwarz, Generalizing Bondy’s theorems on sufficient conditions for Hamiltonian properties, Congr. Numer. 203 (2010) 5-13.
• [2] J.A. Bondy, Longest paths and cycles in graphs of high degree, Research Report CORR 80-16 (Department of Combinatorics and Optimization, Faculty of Mathe- matics, University of Waterloo, Waterloo, Ontario, Canada, 1980).
• [3] J.A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-135. doi:10.1016/0012-365X(76)90078-9[Crossref]
• [4] V. Chvátal and P. Erdős, A note on Hamiltonian circuits, Discrete Math. 2 (1972) 111-113. doi:10.1016/0012-365X(72)90079-9[Crossref]
• [5] G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. s3-2 (1952) 69-81. doi:10.1112/plms/s3-2.1.69[Crossref]
• [6] P. Fraisse, D≥-cycles and their applications for Hamiltonian graphs (LRI, Rapport de Recherche 276, Centre d’Orsay, Université de Paris-Sud, 1986).
• [7] O. Ore, Note on Hamiltonian circuits, Amer. Math. Monthly 67 (1960) 55.
• [8] O. Ore, Hamilton connected graphs, J. Math. Pures Appl. 42 (1963) 21-27.

Identyfikatory

DOI

10.7151/dmgt.1804