A Linear-Time Algorithm for Testing Outer-1-Planarity

A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the ou...

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Bibliographic Details
Published in:	Algorithmica Vol. 72; no. 4; pp. 1033 - 1054
Main Authors:	Hong, Seok-Hee, Eades, Peter, Katoh, Naoki, Liotta, Giuseppe, Schweitzer, Pascal, Suzuki, Yusuke
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.08.2015
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Theory of Computation Graph drawing 1-Planar embedding Outer 1-planar graphs 1-Planarity 1-Planar graphs
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
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Summary:	A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a given graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists.
ISSN:	0178-4617 1432-0541
DOI:	10.1007/s00453-014-9890-8