Edge cycle extendable graphs

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

Abstrakty

EN

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.

Słowa kluczowe

EN

cycle extendable graph; chordal graph; chordless graph; minimally 2-connected graph

Kategorie tematyczne

• 05C38: Paths and cycles
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 2
• Strony: 373-378

Daty

wydano

2012

otrzymano

2010-10-29

poprawiono

2011-06-08

zaakceptowano

2011-06-08

Twórcy

autor

Terry A. McKee

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

Bibliografia

• [1] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes: A Survey (Society for Industrial and Applied Mathematics, Philadelphia, 1999).
• [2] G.A. Dirac, Minimally 2-connected graphs, J. Reine Angew. Math. 228 (1967) 204-216, doi: 10.1515/crll.1967.228.204.
• [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.
• [4] B.Lévêque, F. Maffray and N. Trotignon, On graphs with no induced subdivision of K₄, submitted.
• [5] T.A. McKee, Strongly pancyclic and dual-pancyclic graphs, Discuss. Math. Graph Theory 29 (2009) 5-14, doi: 10.7151/dmgt.1429.
• [6] T.A. McKee and F.R. McMorris, Topics in Intersection Graph Theory (Society for Industrial and Applied Mathematics, Philadelphia, 1999).
• [7] M.D. Plummer, On minimal blocks, Trans. Amer. Math. Soc. 134 (1968) 85-94, doi: 10.1090/S0002-9947-1968-0228369-8.

Identyfikatory

DOI

10.7151/dmgt.1606