Modular and median signpost systems and their underlying graphs

• Autorzy: Henry Martyn Mulder , Ladislav Nebeský
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

signpost system; modular graph; median graph

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C75: Structural characterization of families of graphs
• 05C99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2003
• Tom: 23
• Numer: 2
• Strony: 309-324

Daty

wydano

2003

otrzymano

2001-10-01

poprawiono

2002-04-05

Twórcy

autor

Henry Martyn Mulder

• Econometrisch Instituut, Erasmus Universiteit, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

autor

Ladislav Nebeský

• Filozofická fakulta, Univerzita Karlova v Praze, nám. J. Palacha 2, 116 38 Praha 1, Czech Republic

Bibliografia

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• [3] W. Imrich, S. Klavžar, and H. M. Mulder, Median graphs and triangle-free graphs, SIAM J. Discrete Math. 12 (1999) 111-118, doi: 10.1137/S0895480197323494.
• [4] S. Klavžar and H.M. Mulder, Median graphs: characterizations, location theory and related structures, J. Combin. Math. Combin. Comp. 30 (1999) 103-127.
• [5] H.M. Mulder, The interval function of a graph (Math. Centre Tracts 132, Math. Centre, Amsterdam, 1980).
• [6] L. Nebeský, Graphic algebras, Comment. Math. Univ. Carolinae 11 (1970) 533-544.
• [7] L. Nebeský, Median graphs, Comment. Math. Univ. Carolinae 12 (1971) 317-325.
• [8] L. Nebeský, Geodesics and steps in connected graphs, Czechoslovak Math. Journal 47 (122) (1997) 149-161.
• [9] L. Nebeský, A tree as a finite nonempty set with a binary operation, Mathematica Bohemica 125 (2000) 455-458.
• [10] L. Nebeský, A theorem for an axiomatic approach to metric properties of graphs, Czechoslovak Math. Journal 50 (125) (2000) 121-133.
• [11] M. Sholander, Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3 (1952) 369-381, doi: 10.1090/S0002-9939-1952-0048405-5.

Identyfikatory

DOI

10.7151/dmgt.1204