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Counting realizations of Laman graphs on the sphere

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arxiv 1903.01145 v1 pith:MRJHF5V5 submitted 2019-03-04 math.CO math.AG

Matteo Gallet , Georg Grasegger , Josef Schicho This is my paper · ORCID
classification math.COmath.AG
keywords algorithmlamanrealizationsspacesphereangleschoicechow
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We present an algorithm that computes the number of realizations of a Laman graph on a sphere for a general choice of the angles between the vertices. The algorithm is based on the interpretation of such a realization as a point in the moduli space of stable curves of genus zero with marked points, and on the explicit description, due to Keel, of the Chow ring of this space.

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  1. On the existence of paradoxical motions of generically rigid graphs on the sphere

    math.CO 2019-08 conditional novelty 8.0 of 10

    A graph has a flexible assignment of spherical edge lengths if and only if it admits a NAP-coloring, and K3,3 has exactly three proper spherical motions: two Dixon-type motions and one new constant diagonal angle motion.

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