Extremal families of redundantly rigid graphs in three dimensions

被引：1

作者：

Jordan, Tibor ^{[1
,2
]}

Poston, Christopher ^{[3
]}

Roach, Ryan ^{[4
]}

机构：

[1] Eotvos Lorand Univ, Dept Operat Res, Pazmany Peter setany 1 C, H-1117 Budapest, Hungary

[2] MTA ELTE Egervary Res Grp Combinatorial Optimizat, Pazmany Peter setany 1 C, H-1117 Budapest, Hungary

[3] Yale Univ, Dept Math, New Haven, CT USA

[4] Washington Univ, Dept Math & Stat, St Louis, MO USA

来源：

DISCRETE APPLIED MATHEMATICS | 2022年 / 322卷

基金：

匈牙利科学研究基金会;

关键词：

Rigid graph; Globally rigid graph; Redundant rigidity; Block and hole graph; Rigid framework;

D O I：

10.1016/j.dam.2022.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A rigid graph G is said to be k-vertex (resp. k-edge) rigid in Rd if it remains rigid after the removal of less than k vertices (resp. edges). The definition of k-vertex (resp. k-edge) globally rigid graphs in Rd is similar. We study each of these four versions of redundant (global) rigidity and determine the smallest number of edges in a k-vertex (resp. k-edge) rigid (resp. globally rigid) graph on n vertices in R3 for all positive integers k, except for four special cases, where we provide a close-to-tight bound.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

引用

页码：448 / 464

页数：17

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