## Abstract Let __G__ be an undirected graph without multiple edges and with a loop at every vertex—the set of edges of __G__ corresponds to a reflexive and symmetric binary relation on its set of vertices. Then __every edge‐preserving map of the set of vertices of G to itself fixes an edge__ [{__f
✦ LIBER ✦
A fixed cube theorem for median graphs
✍ Scribed by Hans-Jürgen Bandelt; Marcel van de Vel
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 513 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
The following result is proven: every edge-preserving self-map of a median graph leaves a cube invariant. This extends a fixed edge theorem for trees and parallels a result on invariant simplices in contractible graphs.
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