Properties of uniformly \(3\)-connected graphs (Q6599816)

A graph on at least \(k+1\) vertices is uniformly \(k\)-connected if each pair of its vertices is connected by \(k\) and not more than \(k\) independent paths. The paper shows how the number of vertices of a uniformly 3-connected graph depends on the operations involved in constructing it. Furthermore, the authors show that the bridge operation preserves in a sense crossing numbers and under certain conditions treewidths larger than two, and demonstrate how the results can be used to find out when extremal uniformly 3-connected graphs are planar.