TITLE

# THE i-CHORDS OF CYCLES AND PATHS

AUTHOR(S)
MCKEE, TERRY A.
PUB. DATE
September 2012
SOURCE
Discussiones Mathematicae: Graph Theory;2012, Vol. 32 Issue 4, p607
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
An i-chord of a cycle or path is an edge whose endpoints are a distance i â‰¥ 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 âˆˆ{4, 6}, every cycle C with |V (C)| â‰¥ i has an (i/2)-chord. A graph is a threshold graph if and only if, for i âˆˆ {4, 5}, every path P with |V (P)| = â‰¥ has an (i-2)-chord.
ACCESSION #
82828761

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