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On compact median graphs
Author(s) -
Tardif Claude
Publication year - 1996
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/(sici)1097-0118(199612)23:4<325::aid-jgt1>3.0.co;2-t
Subject(s) - mathematics , combinatorics , endomorphism , automorphism , discrete mathematics , regular polygon , property (philosophy) , graph , intersection (aeronautics) , intersection graph , line graph , geometry , philosophy , epistemology , engineering , aerospace engineering
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 commuting endomorphisms of a compact median graph fixes a common cube. © 1996 John Wiley & Sons, Inc.