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

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NEW SUFFICIENT CONDITIONS FOR HAMILTONIAN AND PANCYCLIC GRAPHS

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

Abstract

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