Weakly modular graphs and nonpositive curvature / Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda.

Format:

Book

Author/Creator:

Chalopin, Jérémie, 1980- author.

Chepoi, Victor, 1961- author.

Hirai, Hiroshi, 1978- author.

Osajda, Damian, 1975- author.

Series:

Memoirs of the American Mathematical Society ; v. 1309.

Memoirs of the American Mathematical Society, 1947-6221 ; v. 1309

Language:

English

Subjects (All):

Graph theory.

Curvature.

Distance geometry.

Combinatorial optimization.

Physical Description:

1 online resource (pages cm.)

Place of Publication:

Providence, RI : American Mathematical Society, [2020]

System Details:

Mode of access : World Wide Web

text file

Summary:

"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 (1-skeletons, collinearity graphs, covering graphs, domains, etc.) in several seemingly-unrelated fields of mathematics: Metric graph theory; Geometric group theory; Incidence geometries and buildings; Theoretical computer science and combinatorial optimization. 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 l1-embeddable weakly modular and sweakly modular graphs we associate high-dimensional cell complexes, having several strong topological and geometrical properties (contractibility and the CAT([empty set]) property). Their cells have a specific structure: they are basis polyhedra of even -matroids in the first case and orthoscheme complexes of gated dual polar subgraphs in the second case. We resolve some open problems concerning subclasses of weakly modular graphs: we prove a Brady-McCammond conjecture about CAT([empty set]) metric on the orthoscheme complexes of modular lattices; we answer Chastand's question about prime graphs for pre-median graphs. We also explore negative curvature for weakly modular graphs"-- Provided by publisher.

Contents:

1. Introduction 2. Preliminaries 3. Local-to-Global Characterization 4. Pre-Median Graphs 5. Dual Polar Graphs 6. Sweakly Modular Graphs 7. Orthoscheme Complexes of Modular Lattices and Semilattices 8. Orthoscheme Complexes of Swm-Graphs 9. Metric Properties of Weakly Modular Graphs

Notes:

"November 2020, volume 268, number 1309 (sixth of 6 numbers)."

Includes bibliographical references.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2020

Description based on print version record.

Other Format:

Print version: Chalopin, Jérémie, 1980- Weakly modular graphs and nonpositive curvature /

ISBN:

9781470463496

Access Restriction:

Restricted for use by site license.