Weakly modular graphs and nonpositive curvature:
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
[2020]
|
| Series: | Memoirs of the American Mathematical Society
1309 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references |
| Physical Description: | vi, 159 Seiten Illustrationen |
| ISBN: | 9781470443627 |
Staff View
MARC
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| 100 | 1 | |a Chalopin, Jérémie |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Weakly modular graphs and nonpositive curvature |c Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c [2020] | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 268, number 1309 (sixth of 6 numbers) | |
| 500 | |a Includes bibliographical references | ||
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| 653 | 0 | |a Curvature | |
| 653 | 0 | |a Distance geometry | |
| 653 | 0 | |a Combinatorial optimization | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1 Introduction
1 1 Avant-propos
1 2 Motivation
1 3 Main results
Acknowledgments
Chapter 2 Preliminaries
2 1 Basic notions
2 2 Further notions
Chapter 3 Local-to-Global Characterization
3 1 Main results
3 2 Weakly modular graphs: proofs
3 3 Helly and clique-Helly graphs: proofs
34A note on meshed graphs
Chapter 4 Pre-Median Graphs
4 1 Main results
4 2 Prime pre-median graphs
4 3 Examples
4 4 L,-Weakly modular graphs
4 5 C(G) is contractible
Chapter 5 Dual Polar Graphs
5 1 Main results
5 2 Proof of Theorem 5 2
5 3 Proof of Theorems 5 3 and 5 4
Chapter 6 Sweakly Modular Graphs
6 1 Main results
62A lattice-theoretical characterization of swm-graphs
6 3 Boolean pairs and Boolean-gated sets
6 4 Barycentric graph G*
6 5 Thickening G*
6 6 A-gates and geodesic extension property
6 7 Normal Boolean-gated paths
6 8 Euclidean buildings of type Cy
6 9 Application I: Biautomaticity of swm-groups
6 10 Application II: 2-approximation to 0-extension problem on
swin-graphs
iii
aoorrr
©
CONTENTS
lv
Chapter 7 Orthoscheme Complexes of Modular Lattices and Semilattices
7 1 Main results
7 2 Boolean and complemented modular lattices
7 3 Distributive and modular lattices
7 4 Proof of Theorem 7 2
7 5 Proof of Propositions 7 5 and 7 6
7 6 Proof of Proposition 7 4
Chapter 8 Orthoscheme Complexes of Swm-Graphs
8 1 Main results
8 2 Examples
8 3 Preliminary results
8 4 1,-metrization
85 l,o-metrization
8 6 lo-metrization
8 7 K(G) is contractible
Chapter 9 Metric Properties of Weakly Modular Graphs
9 1 Quadratic isoperimetric inequality
9 2 Hyperbolicity
9 3 BFS gives a distance-preserving ordering
9 4 Weakly modular complex
Bibliography
|
| adam_txt |
Contents
Chapter 1 Introduction
1 1 Avant-propos
1 2 Motivation
1 3 Main results
Acknowledgments
Chapter 2 Preliminaries
2 1 Basic notions
2 2 Further notions
Chapter 3 Local-to-Global Characterization
3 1 Main results
3 2 Weakly modular graphs: proofs
3 3 Helly and clique-Helly graphs: proofs
34A note on meshed graphs
Chapter 4 Pre-Median Graphs
4 1 Main results
4 2 Prime pre-median graphs
4 3 Examples
4 4 L,-Weakly modular graphs
4 5 C(G) is contractible
Chapter 5 Dual Polar Graphs
5 1 Main results
5 2 Proof of Theorem 5 2
5 3 Proof of Theorems 5 3 and 5 4
Chapter 6 Sweakly Modular Graphs
6 1 Main results
62A lattice-theoretical characterization of swm-graphs
6 3 Boolean pairs and Boolean-gated sets
6 4 Barycentric graph G*
6 5 Thickening G*
6 6 A-gates and geodesic extension property
6 7 Normal Boolean-gated paths
6 8 Euclidean buildings of type Cy
6 9 Application I: Biautomaticity of swm-groups
6 10 Application II: 2-approximation to 0-extension problem on
swin-graphs
iii
aoorrr
©
CONTENTS
lv
Chapter 7 Orthoscheme Complexes of Modular Lattices and Semilattices
7 1 Main results
7 2 Boolean and complemented modular lattices
7 3 Distributive and modular lattices
7 4 Proof of Theorem 7 2
7 5 Proof of Propositions 7 5 and 7 6
7 6 Proof of Proposition 7 4
Chapter 8 Orthoscheme Complexes of Swm-Graphs
8 1 Main results
8 2 Examples
8 3 Preliminary results
8 4 1,-metrization
85 l,o-metrization
8 6 lo-metrization
8 7 K(G) is contractible
Chapter 9 Metric Properties of Weakly Modular Graphs
9 1 Quadratic isoperimetric inequality
9 2 Hyperbolicity
9 3 BFS gives a distance-preserving ordering
9 4 Weakly modular complex
Bibliography |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
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| id | DE-604.BV047362122 |
| illustrated | Illustrated |
| index_date | 2024-07-03T17:41:32Z |
| indexdate | 2024-07-10T09:10:02Z |
| institution | BVB |
| isbn | 9781470443627 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032764078 |
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| physical | vi, 159 Seiten Illustrationen |
| publishDate | 2020 |
| publishDateSearch | 2020 |
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| publisher | American Mathematical Society |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Chalopin, Jérémie Verfasser aut Weakly modular graphs and nonpositive curvature Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda Providence, RI American Mathematical Society [2020] vi, 159 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 268, number 1309 (sixth of 6 numbers) Includes bibliographical references Graphentheorie (DE-588)4113782-6 gnd rswk-swf Graph theory Curvature Distance geometry Combinatorial optimization Graphentheorie (DE-588)4113782-6 s DE-604 Chepoi, Victor aut Hirai, Hiroshi aut Osajda, Damian aut 9781470463496 (pdf) Erscheint auch als Online-Ausgabe 9781-4704-6349-6 Memoirs of the American Mathematical Society 1309 (DE-604)BV008000141 1309 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032764078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chalopin, Jérémie Chepoi, Victor Hirai, Hiroshi Osajda, Damian Weakly modular graphs and nonpositive curvature Memoirs of the American Mathematical Society Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4113782-6 |
| title | Weakly modular graphs and nonpositive curvature |
| title_auth | Weakly modular graphs and nonpositive curvature |
| title_exact_search | Weakly modular graphs and nonpositive curvature |
| title_exact_search_txtP | Weakly modular graphs and nonpositive curvature |
| title_full | Weakly modular graphs and nonpositive curvature Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda |
| title_fullStr | Weakly modular graphs and nonpositive curvature Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda |
| title_full_unstemmed | Weakly modular graphs and nonpositive curvature Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai, Damian Osajda |
| title_short | Weakly modular graphs and nonpositive curvature |
| title_sort | weakly modular graphs and nonpositive curvature |
| topic | Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032764078&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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