Triangulating planar graphs while keeping the Pathwidth small

Abstract

Any simple planar graph can be triangulated, i.e., we can add edges to it, without adding multi-edges, such that the result is planar and all faces are triangles. In this paper, we study the problem of triangulating a planar graph without increasing the pathwidth by much. We show that if a planar graph has pathwidth k, then we can triangulate it so that the resulting graph has pathwidth O(k) (where the factors are 1, 8 and 16 for 3-connected, 2-connected and arbitrary graphs). With similar techniques, we also show that any outer-planar graph of pathwidth k can be turned into a maximal outer-planar graph of pathwidth at most 4k + 4. The previously best known result here was 16k + 15.