@article{0479742fe843444cbfd76ae4b02dbad8,

title = "On the Planar Split Thickness of Graphs",

abstract = "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 graphs, complete bipartite graphs, multipartite graphs, bounded degree graphs, and genus-1 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-splittability in linear time, for a constant k.",

keywords = "Approximation, Complete graphs, Fixed-parameter tractable, Genus-1 graphs, Graph drawing, Graph theory, NP-hardness, Planarity, Splittable, Thickness",

author = "David Eppstein and Philipp Kindermann and Stephen Kobourov and Giuseppe Liotta and Anna Lubiw and Aude Maignan and Debajyoti Mondal and Hamideh Vosoughpour and Sue Whitesides and Stephen Wismath",

note = "Funding Information: Acknowledgements Most of the results of this paper were obtained at the McGill-INRIA-UVictoria 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. Funding Information: Most of the results of this paper were obtained at the McGill-INRIA-UVictoria 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. A preliminary version of this work appeared at the 12th Latin American Theoretical Informatics Symposium (LATIN?16) [10 ]. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2018",

month = mar,

day = "1",

doi = "10.1007/s00453-017-0328-y",

language = "English (US)",

volume = "80",

pages = "977--994",

journal = "Algorithmica",

issn = "0178-4617",

publisher = "Springer New York",

number = "3",

}