DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 23(2) (2003) 309-324
DOI: 10.7151/dmgt.1204

MODULAR AND MEDIAN SIGNPOST SYSTEMS AND THEIR UNDERLYING GRAPHS

Henry Martyn Mulder

Econometrisch Instituut, Erasmus Universiteit
P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
e-mail: hmmulder@few.eur.nl

Ladislav Nebeský1

Filozofická fakulta, Univerzita Karlova v Praze
nám. J. Palacha 2, 116 38 Praha 1, Czech Republic
e-mail: Ladislav.Nebesky@ff.cuni.cz

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.

References

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Received 1 October 2001
Revised 5 April 2002


Footnotes:

1Supported by SWON, Ministry of Education and Science, The Netherlands.