ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 27(1) (2007) 29-38
DOI: 10.7151/dmgt.1341


Ingo Schiermeyer

Fakultät für Mathematik und Informatik
Technische Universität Bergakademie Freiberg
09596 Freiberg, Germany

Mariusz Woźniak

Faculty of Applied Mathematics
AGH University of Science and Technology
Mickiewicza 30, 30-059 Kraków, Poland


For a graph G of order n we consider the unique partition of its vertex set V(G) = A∪B with A = {v ∈ V(G):d(v) ≥ n/2} and B = {v ∈ V(G):d(v) < n/2}. Imposing conditions on the vertices of the set B we obtain new sufficient conditions for hamiltonian and pancyclic graphs.

Keywords: hamiltonian graphs, pancyclic graphs, closure.

2000 Mathematics Subject Classification: 05C38, 05C45.


[1] A. Ainouche and N. Christofides, Semi-independence number of a graph and the existence of hamiltonian circuits, Discrete Appl. Math. 17 (1987) 213-221, doi: 10.1016/0166-218X(87)90025-4.
[2] J.A. Bondy, Pancyclic graphs I, J. Combin. Theory 11 (1971) 80-84, doi: 10.1016/0095-8956(71)90016-5.
[3] J.A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-136, doi: 10.1016/0012-365X(76)90078-9.
[4] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Elsevier North Holland, New York, 1976).
[5] G.A. Dirac, Some theorems on abstract graphs, Proc. London Math. Soc. 2 (1952) 69-81, doi: 10.1112/plms/s3-2.1.69.
[6] R.J. Faudree, R.Häggkvist and R.H. Schelp, Pancyclic graphs - connected Ramsey number, Ars Combin. 11 (1981) 37-49.
[7] E. Flandrin, H. Li, A. Marczyk and M. Woźniak, A note on a new condition implying pancyclism, Discuss. Math. Graph Theory 21 (2001) 137-143, doi: 10.7151/dmgt.1138.
[8] G. Jin, Z. Liu and C. Wang, Two sufficient conditions for pancyclic graphs, Ars Combinatoria 35 (1993) 281-290.
[9] O. Ore, Note on hamilton circuits, Amer. Math. Monthly 67 (1960) 55, doi: 10.2307/2308928.
[10] E.F. Schmeichel and S.L. Hakimi, A cycle structure theorem for hamiltonian graphs, J. Combin. Theory (B) 45 (1988) 99-107, doi: 10.1016/0095-8956(88)90058-5.

Received 1 June 2005
Revised 28 April 2006