Arboreal structure and regular graphs of median-like classes

• Autorzy: Bostjan Brešar
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

median graph; tree; gatedness; amalgam; periphery; regular graph

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2003
• Tom: 23
• Numer: 2
• Strony: 215-225

Daty

wydano

2003

otrzymano

2001-09-26

poprawiono

2002-02-06

Twórcy

autor

Bostjan Brešar

• University of Maribor, FERI, Smetanova 17, 2000 Maribor, Slovenia

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1198