Pairs Of Edges As Chords And As Cut-Edges

• Autorzy: Terry A. McKee
• Języki publikacji: EN

Abstrakty

EN

Several authors have studied the graphs for which every edge is a chord of a cycle; among 2-connected graphs, one characterization is that the deletion of one vertex never creates a cut-edge. Two new results: among 3-connected graphs with minimum degree at least 4, every two adjacent edges are chords of a common cycle if and only if deleting two vertices never creates two adjacent cut-edges; among 4-connected graphs, every two edges are always chords of a common cycle.

Słowa kluczowe

EN

cycle; chord; cut-edge.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2014
• Tom: 34
• Numer: 4
• Strony: 673-681

Daty

wydano

2014-11-01

otrzymano

2013-02-08

poprawiono

2013-09-19

zaakceptowano

2013-09-19

online

2014-11-15

Twórcy

autor

Terry A. McKee

• Department of Mathematics and Statistics Wright State University Dayton, Ohio 45435 USA

Bibliografia

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• [3] R.J. Faudree, Survey of results on k-ordered graphs, Discrete Math. 229 (2001) 73-87. doi:10.1016/S0012-365X(00)00202-8
• [4] W. Gu, X. Jia and H. Wu, Chords in graphs, Australas. J. Combin. 32 (2005) 117-124.
• [5] L. Lovász, Combinatorial Problems and Exercises, Corrected reprint of the 1993 Second Edition (AMS Chelsea Publishing, Providence, 2007).
• [6] K. Menger, Zur allgemeinen Kurventheorie, Fund. Math. 10 (1927) 96-115.
• [7] T.A. McKee, Chords and connectivity, Bull. Inst. Combin. Appl. 47 (2006) 48-52.
• [8] M.D. Plummer, On path properties versus connectivity I , in: Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing, R.C. Mullin, et al. (Ed(s)), (Louisiana State Univ., Baton Rouge, 1971) 457-472.

Identyfikatory

DOI

10.7151/dmgt.1755