ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 16(1) (1996) 27-40
DOI: 10.7151/dmgt.1021


Ralph Faudree

Department of Mathematical Sciences, University of Memphis
Memphis, TN 38152, USA

Odile Favaron
Evelyne Flandrin
Hao Li

L.R.I., URA 410 du C.N.R.S. Bât. 490, Université de Paris-sud
91405-Orsay cedex, France.


We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u)+d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u)+d(v) ≥ n+z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m for each 3 ≤ m ≤ max (dC(u,v)+1, [(n+19)/13]), dC(u,v) being the distance of u and v on a hamiltonian cycle of G.

Keywords: cycle, hamiltonian, pancyclic.

1991 Mathematics Subject Classification: 05C38.


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