Testing Simultaneous Planarity when the Common Graph is 2-Connected
Data Structures and Algorithms
2011-12-12 v2
Abstract
Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a linear-time algorithm to test simultaneous planarity when the two graphs share a 2-connected subgraph. Our algorithm extends to the case of k planar graphs where each vertex [edge] is either common to all graphs or belongs to exactly one of them.
Cite
@article{arxiv.1009.4517,
title = {Testing Simultaneous Planarity when the Common Graph is 2-Connected},
author = {Bernhard Haeupler and Krishnam Raju Jampani and Anna Lubiw},
journal= {arXiv preprint arXiv:1009.4517},
year = {2011}
}
Comments
Appeared in ISAAC 2010, 15 pages, 3 figures