DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 26(2) (2006) 335-342
DOI: 10.7151/dmgt.1324

CHVÁTAL-ERDOS CONDITION AND PANCYCLISM

Evelyne Flandrin,*, Hao Li,*, Antoni Marczykf, Ingo Schiermeyerf and Mariusz Woźniakf

*LRI, UMR 8623, Bât. 490, Université de Paris-Sud
91405 Orsay, France

fAGH University of Science and Technology
Faculty of Applied Mathematics
Al. Mickiewicza 30, 30-059 Kraków, Poland

fFakultät für Mathematik und Informatik
Technische Universität Bergakademie Freiberg
D-09596 Freiberg, Germany

Abstract

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.

Keywords: hamiltonian graphs, pancyclic graphs, cycles, connectivity, stability number.

2000 Mathematics Subject Classification: 05C38, 05C45.

References

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Received 17 February 2005
Revised 21 November 2005