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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1324,
author = {Evelyne Flandrin and Hao Li and Antoni Marczyk and Ingo Schiermeyer and Mariusz Wo\'zniak},
title = {Chv\'atal-Erdos condition and pancyclism},
journal = {Discussiones Mathematicae Graph Theory},
volume = {26},
year = {2006},
pages = {335-342},
zbl = {1142.05049},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1324}
}
Evelyne Flandrin; Hao Li; Antoni Marczyk; Ingo Schiermeyer; Mariusz Woźniak. Chvátal-Erdos condition and pancyclism. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 335-342. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1324/
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