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.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal-lirmm.ccsd.cnrs.fr/lirmm-00904543
Contributor : Dimitrios Thilikos <>
Submitted on : Thursday, November 14, 2013 - 4:23:17 PM
Last modification on : Friday, November 1, 2019 - 11:44:06 AM

Links full text

Identifiers

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

Collections

Citation

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

Share

Metrics

Record views

173