2011/04/30 by Sven Herrmann, Vincent Moulton · 7 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics #Discrete mathematics #Geometry #Mathematics #Point (geometry) #graph theory and CDMA systems #math.CO #math.MG #msc:05C05 #msc:52B11 #msc:54E35 #msc:92D15 #q-bio.QM
paper · pdf · doi:10.1016/j.disc.2012.05.003
published in Discrete Mathematics 312(16), 2506-2521 (Elsevier BV) · 21 pages, 2 figures
openalex publication_date 2012/05/23 · arxiv created 2012/06/06 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Tight-spans of metrics were first introduced by Isbell in 1964 and rediscovered and studied by others, most notably by Dress, who gave them this name. Subsequently, it was found that tight-spans could be defined for more general maps, such as directed metrics and distances, and more recently for diversities. In this paper, we show that all of these tight-spans as well as some related constructions can be defined in terms of point configurations. This provides a useful way in which to study these objects in a unified and systematic way. We also show that by using point configurations we can recover results concerning one-dimensional tight-spans for all of the maps we consider, as well as extend these and other results to more general maps such as symmetric and unsymmetric maps.