# Pairs Of Edges As Chords And As Cut-Edges

Discussiones Mathematicae Graph Theory (2014)

- Volume: 34, Issue: 4, page 673-681
- ISSN: 2083-5892

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topTerry A. McKee. "Pairs Of Edges As Chords And As Cut-Edges." Discussiones Mathematicae Graph Theory 34.4 (2014): 673-681. <http://eudml.org/doc/269818>.

@article{TerryA2014,

abstract = {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.},

author = {Terry A. McKee},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {cycle; chord; cut-edge.; cut-edge},

language = {eng},

number = {4},

pages = {673-681},

title = {Pairs Of Edges As Chords And As Cut-Edges},

url = {http://eudml.org/doc/269818},

volume = {34},

year = {2014},

}

TY - JOUR

AU - Terry A. McKee

TI - Pairs Of Edges As Chords And As Cut-Edges

JO - Discussiones Mathematicae Graph Theory

PY - 2014

VL - 34

IS - 4

SP - 673

EP - 681

AB - 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.

LA - eng

KW - cycle; chord; cut-edge.; cut-edge

UR - http://eudml.org/doc/269818

ER -

## References

top- [1] T. Denley and H. Wu, A generalization of a theorem of Dirac, J. Combin. Theory (B) 82 (2001) 322-326. doi:10.1006/jctb.2001.2041 Zbl1025.05039
- [2] G.A. Dirac, In abstrakten Graphen vorhandene vollständige 4-Graphen und ihre Unterteilungen, Math. Nachr. 22 (1960) 61-85. doi:10.1002/mana.19600220107 Zbl0096.17903
- [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. Zbl1066.05081
- [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.

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