Abstract
Abstract: We show that minimally 3-rigid block-and-hole graphs with one block are characterised as those that are constructible from K 3 by vertex splitting, and also as those having associated looped face graphs that are (3, 0)-tight. This latter property can be verified in polynomial time by a form of pebble game algorithm. We also indicate an application to graph rigidity in 3-dimensional normed spaces that are smooth and strictly convex.
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