Fixed finite subgraph theorems in infinite weakly modular graphs

We prove different fixed subgraph properties for some infinite weakly modular graphs. In particular we prove that every self-contraction (map which preserves or collapses the edges) of a weakly median graph G fixes a non-empty finite regular weakly median subgraph of G if and only if G is connected...

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Bibliographic Details
Published in:Discrete mathematics 2004-08, Vol.285 (1), p.239-256
Main Author: Polat, Norbert
Format: Article
Language:English
Subjects:
Automorphism
Bridged graph
Chordal graph
Combinatorics
Combinatorics. Ordered structures
Endomorphism
Exact sciences and technology
Fixed subgraph theorem
Graph theory
Helly graph
Infinite graph
Mathematics
Sciences and techniques of general use
Simplex
Weakly median graph
Weakly modular graph
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Summary:We prove different fixed subgraph properties for some infinite weakly modular graphs. In particular we prove that every self-contraction (map which preserves or collapses the edges) of a weakly median graph G fixes a non-empty finite regular weakly median subgraph of G if and only if G is connected and contains no infinite simplices and no isometric rays. We also prove some fixed finite simplex theorems for other weakly modular graphs such as Helly graphs, chordal graphs and bridged graphs.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2004.02.018