Medians in median graphs
✍ Scribed by H.J. Bandelt; J.P. Barthélemy
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 668 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0166-218X
No coin nor oath required. For personal study only.
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## Abstract For each vertex __u__ in a connected graph __H__, the __distance__ of __u__ is the sum of the distances from __u__ to each of the vertices __v__ of __H.__ A vertex of minimum distance in __H__ is called a __median__ vertex. It is shown that for any graph __G__ there exists a graph __H__
A median graph is called compact if it does not contain an isometric ray. This property is shown to be equivalent to the finite intersection property for convex sets. We show that a compact median graph contains a finite cube that is fixed by all of its automorphisms, and that each family of commuti
A graph is pseudo-median if for every triple u, v, w of vertices there exists either a unique vertex between each pair of them (if their mutual distances sum up to an even number) or a unique triangle whose edges lie between the three pairs of u, v, w, respectively (if the distance sum is odd). We s
It is shown that a quasi-median graph G without isometric infinite paths contains a Hamming graph (i.e., a cartesian product of complete graphs) which is invariant under any automorphism of G, and moreover if G has no infinite path, then any contraction of G into itself stabilizes a finite Hamming g