Edge cycle extendable graphs

Terry A. McKee

Discussiones Mathematicae Graph Theory (2012)

  • Volume: 32, Issue: 2, page 373-378
  • ISSN: 2083-5892

Abstract

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A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C⁺ is also formed from edges and one chord of a cycle C' of length one greater than C with V(C') ⊆ V(C⁺). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivalently, every chord of a cycle of length five or more has a noncrossing chord.

How to cite

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Terry A. McKee. "Edge cycle extendable graphs." Discussiones Mathematicae Graph Theory 32.2 (2012): 373-378. <http://eudml.org/doc/270896>.

@article{TerryA2012,
abstract = {A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C⁺ is also formed from edges and one chord of a cycle C' of length one greater than C with V(C') ⊆ V(C⁺). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivalently, every chord of a cycle of length five or more has a noncrossing chord.},
author = {Terry A. McKee},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {cycle extendable graph; chordal graph; chordless graph; minimally 2-connected graph},
language = {eng},
number = {2},
pages = {373-378},
title = {Edge cycle extendable graphs},
url = {http://eudml.org/doc/270896},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Terry A. McKee
TI - Edge cycle extendable graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 2
SP - 373
EP - 378
AB - A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C⁺ is also formed from edges and one chord of a cycle C' of length one greater than C with V(C') ⊆ V(C⁺). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivalently, every chord of a cycle of length five or more has a noncrossing chord.
LA - eng
KW - cycle extendable graph; chordal graph; chordless graph; minimally 2-connected graph
UR - http://eudml.org/doc/270896
ER -

References

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  1. [1] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey (Society for Industrial and Applied Mathematics, Philadelphia, 1999). 
  2. [2] G.A. Dirac, Minimally 2-connected graphs, J. Reine Angew. Math. 228 (1967) 204-216, doi: 10.1515/crll.1967.228.204. Zbl0153.25804
  3. [3] R.J. Faudree, R.J. Gould, M.S. Jacobson and L.M. Lesniak, Degree conditions and cycle extendability, Discrete Math. 141 (1995) 109-122, doi: 10.1016/0012-365X(93)E0193-8. Zbl0839.05058
  4. [4] B.Lévêque, F. Maffray and N. Trotignon, On graphs with no induced subdivision of K₄, submitted. Zbl1244.05148
  5. [5] T.A. McKee, Strongly pancyclic and dual-pancyclic graphs, Discuss. Math. Graph Theory 29 (2009) 5-14, doi: 10.7151/dmgt.1429. Zbl1182.05072
  6. [6] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory (Society for Industrial and Applied Mathematics, Philadelphia, 1999). Zbl0945.05003
  7. [7] M.D. Plummer, On minimal blocks, Trans. Amer. Math. Soc. 134 (1968) 85-94, doi: 10.1090/S0002-9947-1968-0228369-8. 

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