Globally rigid graphs are fully reconstructible

نویسندگان

چکیده

Abstract A d -dimensional framework is a pair $(G,p)$ , where $G=(V,E)$ graph and p map from V to $\mathbb {R}^d$ . The length of an edge $uv\in E$ in the distance between $p(u)$ $p(v)$ said be globally rigid if G its lengths uniquely determine up congruence. called every generic rigid. In this paper, we consider problem reconstructing set arising framework. Roughly speaking, strongly reconstructible {C}^d$ (unlabeled) any -space, along with number vertices both association edges lengths. It known that on at least $d+2$ vertices, then it We strengthen result show that, under same conditions, fact fully which means alone sufficient reconstruct without constraint (although still assumption come realization). As key step our proof, also prove rigidity matroid connected. Finally, provide new families graphs use them answer some questions regarding unlabeled reconstructibility posed recent papers.

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ژورنال

عنوان ژورنال: Forum of Mathematics, Sigma

سال: 2022

ISSN: ['2050-5094']

DOI: https://doi.org/10.1017/fms.2022.44