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Article Dans Une Revue Algorithmica Année : 2018

On the Planar Split Thickness of Graphs

Résumé

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.

Dates et versions

hal-01819362 , version 1 (20-06-2018)

Identifiants

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David Eppstein, Philipp Kindermann, Stephen G. Kobourov, Giuseppe Liotta, Anna Lubiw, et al.. On the Planar Split Thickness of Graphs. Algorithmica, 2018, 80 (3), pp.977 - 994. ⟨10.1007/s00453-017-0328-y⟩. ⟨hal-01819362⟩
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