An i-chord of a cycle or path is an edge whose endpoints are a distance i ≥ 2 apart along the cycle or path. Motivated by many standard graph classes being describable by the existence of chords, we investigate what happens when i-chords are required for specific values of i. Results include the following: A graph is strongly chordal if and only if, for i ∈ {4,6}, every cycle C with |V(C)| ≥ i has an (i/2)-chord. A graph is a threshold graph if and only if, for i ∈ {4,5}, every path P with |V(P)| ≥ i has an (i -2)-chord.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1629,
author = {Terry A. McKee},
title = {The i-chords of cycles and paths},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {607-615},
zbl = {1294.05133},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1629}
}
Terry A. McKee. The i-chords of cycles and paths. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 607-615. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1629/
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