Nearly Planar Graphs and {\lambda}-flat Graphs
Combinatorics
2013-11-04 v1
Abstract
A graph G is {\xi}-nearly planar if it can be embedded in the sphere so that each of its edges is crossed at most {\xi} times. The family of {\xi}-nearly planar graphs is widely extending the notion of planarity. We introduce an alternative parameterized graph family extending the notion of planarity, the {\lambda}-flat graphs, this time defined as powers of plane graphs in regard to a novel notion of distance, the wall-by-wall distance. We show that the two parameterized graph classes are parametrically equivalent.
Cite
@article{arxiv.1311.0137,
title = {Nearly Planar Graphs and {\lambda}-flat Graphs},
author = {Alexander Grigoriev and Athanassios Koutsonas and Dimitrios M. Thilikos},
journal= {arXiv preprint arXiv:1311.0137},
year = {2013}
}