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Nearly Planar Graphs and {\lambda}-flat Graphs

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.
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Preprints, Working Papers, ...
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Contributor : Dimitrios Thilikos Connect in order to contact the contributor
Submitted on : Thursday, November 14, 2013 - 4:23:17 PM
Last modification on : Monday, October 11, 2021 - 1:24:06 PM

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  • HAL Id : lirmm-00904543, version 1
  • ARXIV : 1311.0137



Alexander Grigoriev, Athanassios Koutsonas, Dimitrios M. Thilikos. Nearly Planar Graphs and {\lambda}-flat Graphs. 2013. ⟨lirmm-00904543⟩



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