Contracting planar graphs to contractions of triangulations.

Abstract: For every graph H, there exists a polynomial-time algorithm deciding if a planar input graph G can be contracted to H. However, the degree of the polynomial depends on the size of H. We identify a class of graphs such that for every fixed , there exists a linear-time algorithm deciding whether a given planar graph G can be contracted to H. The class is the closure of planar triangulated graphs under taking of contractions. In fact, we prove that a graph if and only if there exists a constant such that if the treewidth of a graph is at least , it contains H as a contraction. We also provide a characterization of in terms of minimal forbidden contractions. [Copyright &y& Elsevier]