Triangulating Planar Graphs While Keeping the Pathwidth Small

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 Ok 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 $$16k+15$$.

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