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

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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.


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Received 1 June 2005
Revised 28 April 2006