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arXiv · 1209.3865

Cubic Augmentation of Planar Graphs

Tanja Hartmann·Jonathan Rollin·Ignaz Rutter
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Abstract

In this paper we study the problem of augmenting a planar graph such that it becomes 3-regular and remains planar. We show that it is NP-hard to decide whether such an augmentation exists. On the other hand, we give an efficient algorithm for the variant of the problem where the input graph has a fixed planar (topological) embedding that has to be preserved by the augmentation. We further generalize this algorithm to test efficiently whether a 3-regular planar augmentation exists that additionally makes the input graph connected or biconnected. If the input graph should become even triconnected, we show that the existence of a 3-regular planar augmentation is again NP-hard to decide.

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Tanja Hartmann, Jonathan Rollin, Ignaz Rutter. 2012-09-18. Cubic Augmentation of Planar Graphs. https://arxiv.org/abs/1209.3865

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