# The i-chords of cycles and paths

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 4, page 607-615
- ISSN: 2083-5892

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topTerry A. McKee. "The i-chords of cycles and paths." Discussiones Mathematicae Graph Theory 32.4 (2012): 607-615. <http://eudml.org/doc/270941>.

@article{TerryA2012,

abstract = {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.},

author = {Terry A. McKee},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {chord; chordal graph; strongly chordal graph; ptolemaic graph; trivially perfect graph; threshold graph; Ptolemaic graph},

language = {eng},

number = {4},

pages = {607-615},

title = {The i-chords of cycles and paths},

url = {http://eudml.org/doc/270941},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Terry A. McKee

TI - The i-chords of cycles and paths

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 4

SP - 607

EP - 615

AB - 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.

LA - eng

KW - chord; chordal graph; strongly chordal graph; ptolemaic graph; trivially perfect graph; threshold graph; Ptolemaic graph

UR - http://eudml.org/doc/270941

ER -

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