On the stability for pancyclicity

• Autorzy: Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

A property P defined on all graphs of order n is said to be k-stable if for any graph of order n that does not satisfy P, the fact that uv is not an edge of G and that G + uv satisfies P implies $d_G(u) + d_G(v) < k$. Every property is (2n-3)-stable and every k-stable property is (k+1)-stable. We denote by s(P) the smallest integer k such that P is k-stable and call it the stability of P. This number usually depends on n and is at most 2n-3. A graph of order n is said to be pancyclic if it contains cycles of all lengths from 3 to n. We show that the stability s(P) for the graph property "G is pancyclic" satisfies max(⎡6n/5]⎤-5, n+t) ≤ s(P) ≤ max(⎡4n/3]⎤-2,n+t), where t = 2⎡(n+1)/2]⎤-(n+1).

Słowa kluczowe

EN

pancyclic graphs; stability

Kategorie tematyczne

• 05C35: Extremal problems
• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2001
• Tom: 21
• Numer: 2
• Strony: 223-228

Daty

wydano

2001

otrzymano

2000-11-15

poprawiono

2001-04-02

Twórcy

autor

Ingo Schiermeyer

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

Bibliografia

• [1] J.A. Bondy, Pancyclic graphs, in: R.C. Mullin, K.B. Reid, D.P. Roselle and R.S.D. Thomas, eds, Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium III (1971) 167-172.
• [2] J.A. Bondy and V. Chvátal, A method in graph theory, Discrete Math. 15 (1976) 111-135, doi: 10.1016/0012-365X(76)90078-9.
• [3] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (Macmillan Press, 1976).
• [4] R. Faudree, O. Favaron, E. Flandrin and H. Li, Pancyclism and small cycles in graphs, Discuss. Math. Graph Theory 16 (1996) 27-40, doi: 10.7151/dmgt.1021.
• [5] U. Schelten and I. Schiermeyer, Small cycles in Hamiltonian graphs, Discrete Applied Math. 79 (1997) 201-211, doi: 10.1016/S0166-218X(97)00043-7.

Identyfikatory

DOI

10.7151/dmgt.1145