@inproceedings{b2627aa8bff540ffa99e8db94c8244f5,

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 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.",

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",

year = "2016",

month = jan,

day = "1",

doi = "10.1007/978-3-662-49529-2_30",

language = "English (US)",

isbn = "9783662495285",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer-Verlag",

pages = "403--415",

editor = "Gonzalo Navarro and Evangelos Kranakis and Edgar Ch{\'a}vez",

booktitle = "LATIN 2016",

note = "12th Latin American Symposium on Theoretical Informatics, LATIN 2016 ; Conference date: 11-04-2016 Through 15-04-2016",

}