On minimal vertex separators of dually chordal graphs: properties and characterizations
Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for ever...
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Lenguaje: | Inglés |
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2012
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Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/83624 |
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I19-R120-10915-83624 |
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Universidad Nacional de La Plata |
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I-19 |
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R-120 |
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SEDICI (UNLP) |
language |
Inglés |
topic |
Matemática Chordal Clique Dually chordal Neighborhood Separator Tree |
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Matemática Chordal Clique Dually chordal Neighborhood Separator Tree De Caria, Pablo Jesús Gutiérrez, Marisa On minimal vertex separators of dually chordal graphs: properties and characterizations |
topic_facet |
Matemática Chordal Clique Dually chordal Neighborhood Separator Tree |
description |
Many works related to dually chordal graphs, their cliques and neighborhoods were published by Brandstädt et al. (1998) and Gutierrez (1996). We will undertake a similar study by considering minimal vertex separators and their properties instead. We find a necessary and sufficient condition for every minimal vertex separator to be contained in the closed neighborhood of a vertex and two major characterizations of dually chordal graphs are proved. The first states that a graph is dually chordal if and only if it possesses a spanning tree such that every minimal vertex separator induces a subtree. The second says that a graph is dually chordal if and only if the family of minimal vertex separators is Helly, its intersection graph is chordal and each of its members induces a connected subgraph. We also found adaptations for them, requiring just O(|E(G)|) minimal vertex separators if they are conveniently chosen. We obtain at the end a proof of a known characterization of the class of hereditary dually chordal graphs that relies on the properties of minimal vertex separators. |
format |
Articulo Articulo |
author |
De Caria, Pablo Jesús Gutiérrez, Marisa |
author_facet |
De Caria, Pablo Jesús Gutiérrez, Marisa |
author_sort |
De Caria, Pablo Jesús |
title |
On minimal vertex separators of dually chordal graphs: properties and characterizations |
title_short |
On minimal vertex separators of dually chordal graphs: properties and characterizations |
title_full |
On minimal vertex separators of dually chordal graphs: properties and characterizations |
title_fullStr |
On minimal vertex separators of dually chordal graphs: properties and characterizations |
title_full_unstemmed |
On minimal vertex separators of dually chordal graphs: properties and characterizations |
title_sort |
on minimal vertex separators of dually chordal graphs: properties and characterizations |
publishDate |
2012 |
url |
http://sedici.unlp.edu.ar/handle/10915/83624 |
work_keys_str_mv |
AT decariapablojesus onminimalvertexseparatorsofduallychordalgraphspropertiesandcharacterizations AT gutierrezmarisa onminimalvertexseparatorsofduallychordalgraphspropertiesandcharacterizations |
bdutipo_str |
Repositorios |
_version_ |
1764820488840806400 |