Pairs Of Edges As Chords And As Cut-Edges

Terry A. McKee

Discussiones Mathematicae Graph Theory (2014)

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

Abstract

top
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.

How to cite

top

Terry 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. [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. [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. [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. [4] W. Gu, X. Jia and H. Wu, Chords in graphs, Australas. J. Combin. 32 (2005) 117-124. Zbl1066.05081
  5. [5] L. Lovász, Combinatorial Problems and Exercises, Corrected reprint of the 1993 Second Edition (AMS Chelsea Publishing, Providence, 2007). 
  6. [6] K. Menger, Zur allgemeinen Kurventheorie, Fund. Math. 10 (1927) 96-115. 
  7. [7] T.A. McKee, Chords and connectivity, Bull. Inst. Combin. Appl. 47 (2006) 48-52. 
  8. [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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.