Metric hypergraphs and metric-line equivalences

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493549" target="_blank" >RIV/00216208:11320/24:10493549 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=u7K6t5Yj7Y" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=u7K6t5Yj7Y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2023.113473" target="_blank" >10.1016/j.disc.2023.113473</a>

Result language
angličtina
Original language name
Metric hypergraphs and metric-line equivalences
Original language description
In a metric space with distance function dist, we say that v is between u and w if u, v, w are pairwise distinct and dist(u, w) = dist(u, v) + dist(v, w). All triples {u, v, w} such that v is between u and w constitute a hypergraph induced by this metric space. In answer to a question posed in [3], we construct an infinite family of 3 -uniform hypergraphs induced by no metric space. The line determined by a pair of distinct points x and y in a metric space is the set consisting of x, y, and all points z such that one of x, y, z is between the remaining two. Two pairs of distinct points are said to be equivalent if they determine the same line. The resulting equivalence relation is a metric -line equivalence. We construct an infinite family of genuinely distinct obstacles that prevent an abstract equivalence relation from being a metric -line equivalence. (c) 2023 Elsevier B.V. All rights reserved.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA22-19073S" target="_blank" >GA22-19073S: Combinatorial and computational complexity in topology and geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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