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arXiv · 1509.03447

On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem

Franz J. Brandenburg
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Abstract

We establish a one-to-one correspondence between 1-planar graphs and general and hole-free 4-map graphs and show that 1-planar graphs can be recognized in polynomial time if they are crossing-augmented, fully triangulated, and maximal 1-planar, respectively, with a polynomial of degree 120, 3, and 5, respectively.

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Franz J. Brandenburg. 2015-09-11. On 4-Map Graphs and 1-Planar Graphs and their Recognition Problem. https://arxiv.org/abs/1509.03447

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