Modular and median signpost systems and their underlying graphs

Henry Martyn Mulder; Ladislav Nebeský

Discussiones Mathematicae Graph Theory (2003)

  • Volume: 23, Issue: 2, page 309-324
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Henry Martyn Mulder, and Ladislav Nebeský. "Modular and median signpost systems and their underlying graphs." Discussiones Mathematicae Graph Theory 23.2 (2003): 309-324. <http://eudml.org/doc/270381>.

@article{HenryMartynMulder2003,
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.},
author = {Henry Martyn Mulder, Ladislav Nebeský},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {signpost system; modular graph; median graph},
language = {eng},
number = {2},
pages = {309-324},
title = {Modular and median signpost systems and their underlying graphs},
url = {http://eudml.org/doc/270381},
volume = {23},
year = {2003},
}

TY - JOUR
AU - Henry Martyn Mulder
AU - Ladislav Nebeský
TI - Modular and median signpost systems and their underlying graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2003
VL - 23
IS - 2
SP - 309
EP - 324
AB - 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.
LA - eng
KW - signpost system; modular graph; median graph
UR - http://eudml.org/doc/270381
ER -

References

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  1. [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. Zbl0099.02201
  2. [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. Zbl0606.05053
  3. [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. Zbl0916.68106
  4. [4] S. Klavžar and H.M. Mulder, Median graphs: characterizations, location theory and related structures, J. Combin. Math. Combin. Comp. 30 (1999) 103-127. Zbl0931.05072
  5. [5] H.M. Mulder, The interval function of a graph (Math. Centre Tracts 132, Math. Centre, Amsterdam, 1980). Zbl0446.05039
  6. [6] L. Nebeský, Graphic algebras, Comment. Math. Univ. Carolinae 11 (1970) 533-544. Zbl0208.02701
  7. [7] L. Nebeský, Median graphs, Comment. Math. Univ. Carolinae 12 (1971) 317-325. Zbl0215.34001
  8. [8] L. Nebeský, Geodesics and steps in connected graphs, Czechoslovak Math. Journal 47 (122) (1997) 149-161. Zbl0898.05041
  9. [9] L. Nebeský, A tree as a finite nonempty set with a binary operation, Mathematica Bohemica 125 (2000) 455-458. Zbl0963.05032
  10. [10] L. Nebeský, A theorem for an axiomatic approach to metric properties of graphs, Czechoslovak Math. Journal 50 (125) (2000) 121-133. Zbl1033.05033
  11. [11] M. Sholander, Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3 (1952) 369-381, doi: 10.1090/S0002-9939-1952-0048405-5. 

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