Arboreal structure and regular graphs of median-like classes

Bostjan Brešar

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 2, page 215-225
  • ISSN: 2083-5892

Abstract

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We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which is a generalization of analogous procedure in median graphs. We characterize regular graphs of these classes whenever they enjoy an additional property. As a corollary we derive that regular weakly median graphs are precisely Cartesian products in which each factor is a complete graph or a hyperoctahedron.

How to cite

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Bostjan Brešar. "Arboreal structure and regular graphs of median-like classes." Discussiones Mathematicae Graph Theory 23.2 (2003): 215-225. <http://eudml.org/doc/270395>.

@article{BostjanBrešar2003,
abstract = {We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which is a generalization of analogous procedure in median graphs. We characterize regular graphs of these classes whenever they enjoy an additional property. As a corollary we derive that regular weakly median graphs are precisely Cartesian products in which each factor is a complete graph or a hyperoctahedron.},
author = {Bostjan Brešar},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {median graph; tree; gatedness; amalgam; periphery; regular graph; Cartesian products},
language = {eng},
number = {2},
pages = {215-225},
title = {Arboreal structure and regular graphs of median-like classes},
url = {http://eudml.org/doc/270395},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Bostjan Brešar
TI - Arboreal structure and regular graphs of median-like classes
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 2
SP - 215
EP - 225
AB - We consider classes of graphs that enjoy the following properties: they are closed for gated subgraphs, gated amalgamation and Cartesian products, and for any gated subgraph the inverse of the gate function maps vertices to gated subsets. We prove that any graph of such a class contains a peripheral subgraph which is a Cartesian product of two graphs: a gated subgraph of the graph and a prime graph minus a vertex. Therefore, these graphs admit a peripheral elimination procedure which is a generalization of analogous procedure in median graphs. We characterize regular graphs of these classes whenever they enjoy an additional property. As a corollary we derive that regular weakly median graphs are precisely Cartesian products in which each factor is a complete graph or a hyperoctahedron.
LA - eng
KW - median graph; tree; gatedness; amalgam; periphery; regular graph; Cartesian products
UR - http://eudml.org/doc/270395
ER -

References

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