Discussiones Mathematicae Graph Theory 32(2) (2012) 373-378
doi: 10.7151/dmgt.1606

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Edge Cycle Extendable Graphs

Terry A. McKee

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

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.

Keywords: cycle extendable graph, chordal graph, chordless graph, minimally 2-connected graph

2010 Mathematics Subject Classification: 05C75, 05C38.

References

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Received 29 October 2010
Revised 8 June 2011
Accepted 8 June 2011