ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2017-2018): c. 84%
Mathematicae Graph Theory 21(1) (2001) 137-143DOI: 10.7151/dmgt.1138
LRI, Bât. 490
Université de Paris-Sud
91405 Orsay, France
Faculty of Applied Mathematics AGH
Al. Mickiewicza 30, 30-059 Kraków, Poland
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.
Received 15 November 2000
Revised 13 December 2000