Abstract
We showed in the first paper of this series that the generic C1-cofactor matroid is the unique maximal abstract 3-rigidity matroid. In this paper we obtain a combinatorial characterization of independence in this matroid. This solves the cofactor counterpart of the combinatorial characterization problem for the rigidity of generic 3-dimensional bar-joint frameworks. We use our characterization to verify that the counterparts of conjectures of Dress (on the rank function) and Lovász and Yemini (which suggested a sufficient connectivity condition for rigidity) hold for the C1-cofactor matroid.
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© 2023. The Authors. Published by Diamond Open Access Journals