DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

DOI 10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 21(1) (2001) 137-143
DOI: 10.7151/dmgt.1138

A NOTE ON A NEW CONDITION IMPLYING PANCYCLISM

Evelyne Flandrin
Hao Li

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

Antoni Marczyk
Mariusz Woźniak

Faculty of Applied Mathematics AGH
Al. Mickiewicza 30, 30-059 Kraków, Poland

Abstract

We first show that if a 2-connected graph G of order n is such that for each two vertices u and v such that δ = d(u) and d(v) < n/2 the edge uv belongs to E(G), then G is hamiltonian. Next, by using this result, we prove that a graph G satysfying the above condition is either pancyclic or isomorphic to Kn/2,n/2.

Keywords: hamiltonian graphs, pancyclic graphs, cycles.

2000 Mathematics Subject Classification: 05C38, 05C45.

References

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Received 15 November 2000
Revised 13 December 2000