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ArticleOriginal scientific text

Title

Arboreal structure and regular graphs of median-like classes

Authors 1

Affiliations

  1. University of Maribor, FERI, Smetanova 17, 2000 Maribor, Slovenia

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.

Keywords

ENG
median graph, tree, gatedness, amalgam, periphery, regular graph

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Discussiones Mathematicae Graph Theory
2003/23/2
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Pages:
215-225
Main language of publication
English
Received
2001-09-26
Accepted
2002-02-06
Published
2003

DOI: 10.7151/dmgt.1198

Exact and natural sciences