Whitney triangulations, local girth and iterated clique graphs (Q1850046)

The authors study the dynamical behaviour of surface triangulations under the iterated application of the clique graph operator \(k\), which transforms a graph \(H\) into the intersection graph \(kH\) of its maximal cliques. A graph \(G\) is \(k\)-divergent if the sequence of the orders \(|V(k^n G)|\) tends to infinity with \(n\). Otherwise, \(G\) is \(k\)-bounded. It is assumed that every triangle of \(G\) is a face of the triangulation and it is proved that every such \(d\)-regular triangulation is \(k\)-bounded for \(d\geq 7\).