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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1606,
author = {Terry A. McKee},
title = {Edge cycle extendable graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {373-378},
zbl = {1255.05162},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1606}
}
Terry A. McKee. Edge cycle extendable graphs. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 373-378. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1606/
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