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Discussiones Mathematicae Graph Theory 23(2) (2003) 309-324
DOI: https://doi.org/10.7151/dmgt.1204
MODULAR AND MEDIAN SIGNPOST SYSTEMS AND THEIR UNDERLYING GRAPHS
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Henry Martyn Mulder
Econometrisch Instituut, Erasmus Universiteit |
Ladislav Nebeský1
Filozofická fakulta, Univerzita Karlova v Praze |
Abstract
The concept of a signpost system on a set is introduced. It is a ternary relation on the set satisfying three fairly natural axioms. Its underlying graph is introduced. When the underlying graph is disconnected some unexpected things may happen. The main focus are signpost systems satisfying some extra axioms. Their underlying graphs have lots of structure: the components are modular graphs or median graphs. Yet another axiom guarantees that the underlying graph is also connected. The main results of this paper concern if-and-only-if characterizations involving signpost systems satisfying additional axioms on the one hand and modular, respectively median graphs on the other hand.Keywords: signpost system, modular graph, median graph.
2000 Mathematics Subject Classification: 05C99, 05C12, 05C75.
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Received 1 October 2001
Revised 5 April 2002