Universität zu Köln

Schrader, Rainer ORCID: 0000-0001-6635-0132 and Stenmans, Lukas (2020). A de Bruijn-Erdos Theorem for (q, q-4)-graphs. Discret Appl. Math., 279. S. 198 - 202. AMSTERDAM: ELSEVIER. ISSN 1872-6771

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Abstract

Based on a ternary betweenness relation, Coxeter introduced the notion of a line in ordered geometries. Later, Chen and Chvatal observed that in particular the distance function of a finite metric space induces a betweenness relation. They conjecture that in every metric space on n points either all points lie on one line or there exist n mutually distinct lines. A weaker version conjectures that this holds for every finite graph on n vertices with the graph-theoretic distance. We prove this conjecture for (q, q-4)-graphs. (C) 2019 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schrader, Rainer UNSPECIFIED orcid.org/0000-0001-6635-0132 UNSPECIFIED Stenmans, Lukas UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-332545
DOI:	10.1016/j.dam.2019.11.008
Journal or Publication Title:	Discret Appl. Math.
Volume:	279
Page Range:	S. 198 - 202
Date:	2020
Publisher:	ELSEVIER
Place of Publication:	AMSTERDAM
ISSN:	1872-6771
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Institute of Computer Science
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language GRAPHS Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/33254