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2024 | OriginalPaper | Chapter

Characterizing s-Strongly Chordal Graphs Using 2-Paths and k-Chords

Author : Terry A. McKee

Published in: Combinatorics, Graph Theory and Computing

Publisher: Springer Nature Switzerland

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Abstract

A well-known 1961 characterization of chordal graphs by G. A. Dirac in terms of simplicial vertices, was extended by Chvátal, Rusu, and Sritharan (Discrete Math., 2002) to a natural sequence of “weakly chordal graphs.” Somewhat similarly, we will start from the same place and characterize a natural sequence of “chordal, strongly chordal, …, s-strongly chordal, …” graphs, except now in terms of 2-path graphs (meaning graphs that are either \(K_3\) or a 2-tree graph with exactly two degree-2 vertices—equivalently, “paths of triangles” that are the 2-connected outerplanar strongly chordal graphs).

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previous chapter Geodesic Leech Graphs
next chapter The Spectrum Problem for the 4-Uniform 4-Colorable 3-Cycles with Maximum Degree 2
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Metadata
Title
Characterizing s-Strongly Chordal Graphs Using 2-Paths and k-Chords
Author
Terry A. McKee
Copyright Year
2024
Book
Combinatorics, Graph Theory and Computing

Print ISBN: 978-3-031-62165-9

Electronic ISBN: 978-3-031-62166-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-62166-6_17

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