Characterizing minimally flat symmetric hypergraphs

Kaszanitzky, Viktoria Eszter and Schulze, Bernd (2018) Characterizing minimally flat symmetric hypergraphs. Discrete Applied Mathematics, 236. pp. 256-269. ISSN 0166-218X

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In Kaszanitzky and Schulze (2017) we gave necessary conditions for a symmetric d-picture (i.e., a symmetric realization of an incidence structure in Rd) to be minimally flat, that is, to be non-liftable to a polyhedral scene without having redundant constraints. These conditions imply very simply stated restrictions on the number of those structural components of the picture that are fixed by the elements of its symmetry group. In this paper we show that these conditions on the fixed structural components, together with the standard non-symmetric counts, are also sufficient for a plane picture which is generic with three-fold rotational symmetry C3 to be minimally flat. This combinatorial characterization of minimally flat C3-generic pictures is obtained via a new inductive construction scheme for symmetric sparse hypergraphs. We also give a sufficient condition for sharpness of pictures with C3 symmetry.

Item Type:
Journal Article
Journal or Publication Title:
Discrete Applied Mathematics
Additional Information:
This is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Applied Mathematics, 236, 2018 DOI: 10.1016/j.dam.2017.11.017
Uncontrolled Keywords:
?? incidence structurepicturepolyhedral sceneliftingsymmetrysparse hypergraphdiscrete mathematics and combinatoricsapplied mathematics ??
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Deposited On:
20 Nov 2017 21:30
Last Modified:
15 Jul 2024 17:20