Triangulating planar graphs while minimizing the maximum degree

Abstract

In this paper we study the problem of triangulating a planar graph G while minimizing the maximum degree Δ(G') of the resulting triangulated planar graph (G'). It is shown that this problem is NP-complete. Worst-case lower bounds for Δ(G') with respect to Δ(G) are given. We describe a linear algorithm to triangulate planar graphs, for which the maximum degree of the triangulated graph is only a constant larger than the lower bounds. Finally we show that triangulating one face while minimizing the maximum degree can be achieved in polynomial time. We use this algorithm to obtain a polynomial exact algorithm to triangulate the interior faces of an outerplanar graph while minimizing the maximum degree