Recognizing Optimal 1-Planar Graphs in Linear Time
Discrete Mathematics
2018-01-25 v1
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.
Cite
@article{arxiv.1602.08022,
title = {Recognizing Optimal 1-Planar Graphs in Linear Time},
author = {Franz J. Brandenburg},
journal= {arXiv preprint arXiv:1602.08022},
year = {2018}
}
Comments
32 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:1602.06407