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arXiv · 1602.08022

Recognizing Optimal 1-Planar Graphs in Linear Time

Franz J. Brandenburg
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Abstract

A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8 edges. We show that optimal 1-planar graphs can be recognized in linear time. Our algorithm implements a graph reduction system with two rules, which can be used to reduce every optimal 1-planar graph to an irreducible extended wheel graph. The graph reduction system is non-deterministic, constraint, and non-confluent.

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Franz J. Brandenburg. 2016-02-25. Recognizing Optimal 1-Planar Graphs in Linear Time. https://doi.org/10.1007/s00453-016-0226-8

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