PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2003 | 23 | 2 | 309-324
Tytuł artykułu

Modular and median signpost systems and their underlying graphs

Treść / Zawartość
Warianty tytułu
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
Wydawca
Rocznik
Tom
23
Numer
2
Strony
309-324
Opis fizyczny
Daty
wydano
2003
otrzymano
2001-10-01
poprawiono
2002-04-05
Twórcy
  • Econometrisch Instituut, Erasmus Universiteit, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
  • Filozofická fakulta, Univerzita Karlova v Praze, nám. J. Palacha 2, 116 38 Praha 1, Czech Republic
Bibliografia
  • [1] S.P. Avann, Metric ternary distributive semi-lattices, Proc. Amer. Math. Soc. 11 (1961) 407-414, doi: 10.1090/S0002-9939-1961-0125807-5.
  • [2] H.-J. Bandelt and H.M. Mulder, Pseudo-modular graphs, Discrete Math. 62 (1986) 245-260, doi: 10.1016/0012-365X(86)90212-8.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1204
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.