# Arboreal structure and regular graphs of median-like classes

Discussiones Mathematicae Graph Theory (2003)

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

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topBostjan 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 -

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