Requiring that Minimal Separators Induce Complete Multipartite Subgraphs

Terry A. McKee

Discussiones Mathematicae Graph Theory (2018)

  • Volume: 38, Issue: 1, page 263-273
  • ISSN: 2083-5892

Abstract

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Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the classical chordal graphs and the emergent unichord-free graphs. New theorems characterize several subclasses of the graphs whose minimal separators induce complete multipartite subgraphs, in particular the graphs that are 2-clique sums of complete, cycle, wheel, and octahedron graphs.

How to cite

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Terry A. McKee. "Requiring that Minimal Separators Induce Complete Multipartite Subgraphs." Discussiones Mathematicae Graph Theory 38.1 (2018): 263-273. <http://eudml.org/doc/288415>.

@article{TerryA2018,
abstract = {Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the classical chordal graphs and the emergent unichord-free graphs. New theorems characterize several subclasses of the graphs whose minimal separators induce complete multipartite subgraphs, in particular the graphs that are 2-clique sums of complete, cycle, wheel, and octahedron graphs.},
author = {Terry A. McKee},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {minimal separator; complete multipartite graph; chordal graph; unichord-free graph},
language = {eng},
number = {1},
pages = {263-273},
title = {Requiring that Minimal Separators Induce Complete Multipartite Subgraphs},
url = {http://eudml.org/doc/288415},
volume = {38},
year = {2018},
}

TY - JOUR
AU - Terry A. McKee
TI - Requiring that Minimal Separators Induce Complete Multipartite Subgraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2018
VL - 38
IS - 1
SP - 263
EP - 273
AB - Complete multipartite graphs range from complete graphs (with every partite set a singleton) to edgeless graphs (with a unique partite set). Requiring minimal separators to all induce one or the other of these extremes characterizes, respectively, the classical chordal graphs and the emergent unichord-free graphs. New theorems characterize several subclasses of the graphs whose minimal separators induce complete multipartite subgraphs, in particular the graphs that are 2-clique sums of complete, cycle, wheel, and octahedron graphs.
LA - eng
KW - minimal separator; complete multipartite graph; chordal graph; unichord-free graph
UR - http://eudml.org/doc/288415
ER -

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