Weakly Modular Graphs and Nonpositive Curvature

This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive curvature" and “local-to-global” properties and characterizatio...

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Hlavní autoři: Chalopin, Jérémie, Chepoi, Victor, Hirai, Hiroshi, Osajda, Damian
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2020
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Curvature
Distance geometry
Graph theory
combinatorial optimization
lattice
nonpositive curvature
CAT space
incidence geometry
Weakly modular graph
group action
building
ISBN:9781470443627, 1470443627
ISSN:0065-9266, 1947-6221
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Shrnutí:This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various “nonpositive curvature" and “local-to-global” properties and characterizations of weakly modular graphs and their subclasses. Weakly modular graphs have been introduced as a far-reaching common generalization of median graphs (and more generally, of modular and orientable modular graphs), Helly graphs, bridged graphs, and dual polar graphs occurring under different disguises ( We give a local-to-global characterization of weakly modular graphs and their subclasses in terms of simple connectedness of associated triangle-square complexes and specific local combinatorial conditions. In particular, we revisit characterizations of dual polar graphs by Cameron and by Brouwer-Cohen. We also show that (disk-)Helly graphs are precisely the clique-Helly graphs with simply connected clique complexes. With
Bibliografie:Includes bibliographical references (p. 155-159)
November 2020, volume 268, number 1309 (sixth of 6 numbers)
ISBN:9781470443627
1470443627
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1309