Characterizing Atoms that Result from Decomposition by Clique Separators

Terry A. McKee

Discussiones Mathematicae Graph Theory (2017)

  • Volume: 37, Issue: 3, page 587-594
  • ISSN: 2083-5892

Abstract

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A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph).

How to cite

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Terry A. McKee. "Characterizing Atoms that Result from Decomposition by Clique Separators." Discussiones Mathematicae Graph Theory 37.3 (2017): 587-594. <http://eudml.org/doc/288422>.

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abstract = {A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph).},
author = {Terry A. McKee},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {clique separator; minimal separator; unichord-free graph},
language = {eng},
number = {3},
pages = {587-594},
title = {Characterizing Atoms that Result from Decomposition by Clique Separators},
url = {http://eudml.org/doc/288422},
volume = {37},
year = {2017},
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AU - Terry A. McKee
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JO - Discussiones Mathematicae Graph Theory
PY - 2017
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SP - 587
EP - 594
AB - A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition. Atoms are characterized here in two ways: first using generalized vertex elimination schemes, and then as generalizations of 2-connected unichord-free graphs (the graphs in which every minimal vertex separator induces an edgeless subgraph).
LA - eng
KW - clique separator; minimal separator; unichord-free graph
UR - http://eudml.org/doc/288422
ER -

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