On plane rigidity matroids

A graph embedded in \(R^d\) as a framework of bars and joints is said to be rigid if it does not admit any continuous motion other than the isometries of the entire space.
While for \(d=1\) rigidity is essentially connectivity, a much richer theory is encountered already for \(d=2\).

In my talk I will recall some basic notions of rigidity theory and introduce the relevant graphs and matroids. I will then present some new results. One of them is a purely combinatorial statement about cubic graphs, for which we currently do not have a combinatorial proof.