On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs Fan-planar graphs were recently introduced as a generalization of 1-planar graphs. A graph is fan-planar if it can be embedded in the plane, such that each edge that is crossed more than once, is crossed by a bundle of two or more edges incident to a common vertex. A graph is outer-fan-planar if it has a fan-planar embedding in which every vertex is on the outer face. If, in addition, the insertion of an edge destroys its outer-fan-planarity, then it is maximal outer-fan-planar. In this paper, we present a linear-time algorithm to test whether a given graph is maximal outer-fan-planar. The algorithm can also be employed to produce an outer-fan-planar embedding, if one exists. On the negative side, we show that testing fan-planarity of a graph is NP-complete, for the case where the rotation system (i.e., the cyclic order of the edges around each vertex) is given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algorithmica Springer Journals

On the Recognition of Fan-Planar and Maximal Outer-Fan-Planar Graphs

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Computer Science; Algorithm Analysis and Problem Complexity; Theory of Computation; Mathematics of Computing; Algorithms; Computer Systems Organization and Communication Networks; Data Structures, Cryptology and Information Theory
ISSN
0178-4617
eISSN
1432-0541
D.O.I.
10.1007/s00453-016-0200-5
Publisher site
See Article on Publisher Site

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