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2006 | 26 | 2 | 335-342
Tytuł artykułu

Chvátal-Erdos condition and pancyclism

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The well-known Chvátal-Erdős theorem states that if the stability number α of a graph G is not greater than its connectivity then G is hamiltonian. In 1974 Erdős showed that if, additionally, the order of the graph is sufficiently large with respect to α, then G is pancyclic. His proof is based on the properties of cycle-complete graph Ramsey numbers. In this paper we show that a similar result can be easily proved by applying only classical Ramsey numbers.
Wydawca
Rocznik
Tom
26
Numer
2
Strony
335-342
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-02-17
poprawiono
2005-11-21
Twórcy
  • LRI, UMR 8623, Bât. 490, Université de Paris-Sud, 91405 Orsay, France
autor
  • LRI, UMR 8623, Bât. 490, Université de Paris-Sud, 91405 Orsay, France
  • AGH University of Science and Technology, Faculty of Applied Mathematics, Al. Mickiewicza 30, 30-059 Kraków, Poland
  • Fakultät für Mathematik und Informatik, Technische Universität Bergakademie Freiberg, D-09596 Freiberg, Germany
  • AGH University of Science and Technology, Faculty of Applied Mathematics, Al. Mickiewicza 30, 30-059 Kraków, Poland
Bibliografia
  • [1] D. Amar, I. Fournier and A. Germa, Pancyclism in Chvátal-Erdős graphs, Graphs Combin. 7 (1991) 101-112, doi: 10.1007/BF01788136.
  • [2] J.A. Bondy, Pancyclic graphs I, J. Combin. Theory 11 (1971) 80-84, doi: 10.1016/0095-8956(71)90016-5.
  • [3] J.A. Bondy, Pancyclic graphs, in: Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing (1971) 167-172.
  • [4] J.A. Bondy and P. Erdős, Ramsey numbers for cycles in graphs, J. Combin. Theory (B) 14 (1973) 46-54, doi: 10.1016/S0095-8956(73)80005-X.
  • [5] J.A. Bondy and U.S.R. Murty, Graphs Theory with Applications (Macmillan. London, 1976).
  • [6] S. Brandt, private communication.
  • [7] S. Brandt, R. Faudree and W. Goddard, Weakly pancyclic graphs, J. Graph Theory 27 (1998) 141-176, doi: 10.1002/(SICI)1097-0118(199803)27:3<141::AID-JGT3>3.0.CO;2-O
  • [8] V. Chvátal, P. Erdős, A note on Hamilton circuits, Discrete Math. 2 (1972) 111-113, doi: 10.1016/0012-365X(72)90079-9.
  • [9] N. Chakroun and D. Sotteau, Chvátal-Erdős theorem for digraphs, in: Cycles and Rays (Montreal, 1987) (Kluwer, Dordrecht, 1990) 75-86.
  • [10] P. Erdős, On the construction of certain graphs, J. Combin. Theory 1 (1966) 149-152, doi: 10.1016/S0021-9800(66)80011-X.
  • [11] P. Erdős, Some problems in Graph Theory, in: Lecture Notes Math. 411 (1974) 187-190.
  • [12] B. Jackson and O. Ordaz, Chvátal-Erdős condition for path and cycles in graphs and digraphs. A survey, Discrete Math. 84 (1990) 241-254, doi: 10.1016/0012-365X(90)90130-A.
  • [13] D. Lou, The Chvátal-Erdős condition for cycles in triangle-free graphs, Discrete Math. 152 (1996) 253-257, doi: 10.1016/0012-365X(96)80461-4.
  • [14] A. Marczyk and J-F. Saclé, On the Jackson-Ordaz conjecture for graphs with the stability number four (Rapport de Recherche 1287, Université de Paris-Sud, Centre d'Orsay, 2001).
  • [15] F.P. Ramsey, On a Problem of Formal Logic, Proc. London Math. Soc. 30 (1930) 264-286, doi: 10.1112/plms/s2-30.1.264.
  • [16] S. Zhang, Pancyclism and bipancyclism of hamiltonian graphs, J. Combin. Theory (B) 60 (1994) 159-168, doi: 10.1006/jctb.1994.1010.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1324
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