TY - GEN

T1 - On the planar split thickness of graphs

AU - Eppstein, David

AU - Kindermann, Philipp

AU - Kobourov, Stephen

AU - Liotta, Giuseppe

AU - Lubiw, Anna

AU - Maignan, Aude

AU - Mondal, Debajyoti

AU - Vosoughpour, Hamideh

AU - Whitesides, Sue

AU - Wismath, Stephen

N1 - Funding Information:
Most of the results of this paper were obtained at the McGill-INRIA-Victoria Workshop on Computational Geometry, Barbados, February 2015. We would like to thank the organizers of these events, as well as many participants for fruitful discussions and suggestions. The first, fourth, sixth, and eighth authors acknowledge the support from NSF grant 1228639, 2012C4E3KT PRIN Italian National Research Project, PEPS egalite project, and NSERC respectively.
Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.

PY - 2016

Y1 - 2016

N2 - Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest k such that the graph is k-splittable into a planar graph. A k-split operation substitutes a vertex v by at most k new vertices such that each neighbor of v is connected to at least one of the new vertices. We first examine the planar split thickness of complete and complete bipartite graphs. We then prove that it is NP-hard to recognize graphs that are 2-splittable into a planar graph, and show that one can approximate the planar split thickness of a graph within a constant factor. If the treewidth is bounded, then we can even verify k-splittablity in linear time, for a constant k.

AB - Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest k such that the graph is k-splittable into a planar graph. A k-split operation substitutes a vertex v by at most k new vertices such that each neighbor of v is connected to at least one of the new vertices. We first examine the planar split thickness of complete and complete bipartite graphs. We then prove that it is NP-hard to recognize graphs that are 2-splittable into a planar graph, and show that one can approximate the planar split thickness of a graph within a constant factor. If the treewidth is bounded, then we can even verify k-splittablity in linear time, for a constant k.

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U2 - 10.1007/978-3-662-49529-2_30

DO - 10.1007/978-3-662-49529-2_30

M3 - Conference contribution

AN - SCOPUS:84961683199

SN - 9783662495285

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 403

EP - 415

BT - LATIN 2016

A2 - Navarro, Gonzalo

A2 - Kranakis, Evangelos

A2 - Chávez, Edgar

PB - Springer-Verlag

T2 - 12th Latin American Symposium on Theoretical Informatics, LATIN 2016

Y2 - 11 April 2016 through 15 April 2016

ER -