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Titel:

On the Planar Split Thickness of Graphs

AutorInnen:

David Eppstein
Philipp Kindermann
Stephen Kobourov
Giuseppe Liotta
Anna Lubiw
Aude Maignan
Debajyoti Mondal
Hamideh Vosoughpour
Sue Whitesides
Stephen Wismath

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Artikel in Zeitschriften

erschienen in:

Algorithmica, Special Issue on Selected Papers from LATIN'16, Vol. 80, no. 3, 2018, pp. 977-994.

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.

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BibTeX-Eintrag:

@Article{ekkllmmvww-opstg-A18, 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}, title = {On the Planar Split Thickness of Graphs}, journal = {Algorithmica}, year = {2018}, volume = {80}, number = {,}, pages = {977--994}, note = {Special Issue on Theoretical Informatics}, 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 $k$.}, doi = {10.1007/s00453-017-0328-y}, }