New sufficient conditions for hamiltonian and pancyclic graphs

• Autorzy: Ingo Schiermeyer , Mariusz Woźniak
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hamiltonian graphs; pancyclic graphs; closure

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 29-38

Daty

wydano

2007

otrzymano

2005-06-01

poprawiono

2006-04-28

Twórcy

autor

Ingo Schiermeyer

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

autor

Mariusz Woźniak

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1341