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C-Planarity of Embedded Cyclic c-Graphs

  • Radoslav Fulek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9801)

Abstract

We show that c-planarity is solvable in quadratic time for flat clustered graphs with three clusters if the combinatorial embedding of the underlying graph is fixed. In simpler graph-theoretical terms our result can be viewed as follows. Given a graph G with the vertex set partitioned into three parts embedded on a 2-sphere, our algorithm decides if we can augment G by adding edges without creating an edge-crossing so that in the resulting spherical graph the vertices of each part induce a connected sub-graph. We proceed by a reduction to the problem of testing the existence of a perfect matching in planar bipartite graphs. We formulate our result in a slightly more general setting of cyclic clustered graphs, i.e., the simple graph obtained by contracting each cluster, where we disregard loops and multi-edges, is a cycle.

Notes

Acknowledgment

I would like to thank Jan Kynčl and Dömötör Pálvölgyi for many comments and suggestions that helped to improve the presentation of the result.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.IST AustriaKlosterneuburgAustria

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