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Pairs Of Edges As Chords And As Cut-Edges

100%

McKee T. A.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 4

673-681

Several authors have studied the graphs for which every edge is a chord of a cycle; among 2-connected graphs, one characterization is that the deletion of one vertex never creates a cut-edge. Two new results: among 3-connected graphs with minimum degree at least 4, every two adjacent edges are chords of a common cycle if and only if deleting two vertices never creates two adjacent cut-edges; among 4-connected graphs, every two edges are always chords of a common cycle.

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The i-chords of cycles and paths

75%

McKee T.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 4

607-615

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.

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2 Discussiones Mathematicae Graph Theory

1 McKee T.

1 McKee T. A.

1 2014

1 2012

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Pairs Of Edges As Chords And As Cut-Edges

The i-chords of cycles and paths