组合伪三角剖分
组合数学
2007-05-24 v3 度量几何
摘要
我们证明一个平面图在平面内是泛型刚性的当且仅当它可嵌入为一个伪三角剖分。这推广了 math.CO/0307347 的主要结果，该文处理极小泛型刚性情形。证明使用了平面中的组合伪三角剖分（CPT）概念，并有两个主要步骤：证明某一“广义 Laman 性质”是 CPT 为“可拉伸”的充要条件，以及证明所有泛型刚性平面图都容许具有该性质的 CPT 指派。此外，我们提出对闭曲面上的组合伪三角剖分的研究。
引用
@article{arxiv.math/0307370,
title = {Combinatorial pseudo-Triangulations},
author = {David Orden and Francisco Santos and Brigitte Servatius and Herman Servatius},
journal= {arXiv preprint arXiv:math/0307370},
year = {2007}
}
备注
17 pages, 10 figures. Changes from v2: minor editing plus removal of a superfluous lemma. Changes from v1: Section 5 has been completely rewritten, after a referee complained (rightfully) that too many details were omitted. The rest only has minor corrections and stylistic changes. This version has been accepted in "Discrete Mathematics"