Universität zu Köln

Fowler, J. Joseph, Juenger, Michael, Kobourov, Stephen G. and Schulz, Michael (2011). Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges. Comput. Geom.-Theory Appl., 44 (8). S. 385 - 399. AMSTERDAM: ELSEVIER SCIENCE BV. ISSN 0925-7721

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Abstract

A set of planar graphs {G(1) (V, E-1), ..., G(k)(V, E-k)} admits a simultaneous embedding if they can be drawn on the same pointset P of order n in the Euclidean plane such that each point in P corresponds one-to-one to a vertex in V and each edge in E-i does not cross any other edge in E-i (except at endpoints) for i is an element of {1, ..., k}. A fixed edge is an edge (u, v) that is drawn using the same simple curve for each graph G(i) whose edge set E-i contains the edge (u, v). We give a necessary and sufficient condition for two graphs whose union is homeomorphic to K-5 or K-3,K-3 to admit a simultaneous embedding with fixed edges (SEFE). This allows us to characterize the class of planar graphs that always have a SEFE with any other planar graph. We also characterize the class of biconnected outerplanar graphs that always have a SEFE with any other outerplanar graph. In both cases, we provide O(n(4))-time algorithms to compute a SEFE. (C) 2011 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Fowler, J. Joseph UNSPECIFIED UNSPECIFIED UNSPECIFIED Juenger, Michael UNSPECIFIED UNSPECIFIED UNSPECIFIED Kobourov, Stephen G. UNSPECIFIED UNSPECIFIED UNSPECIFIED Schulz, Michael UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-488759
DOI:	10.1016/j.comgeo.2011.02.002
Journal or Publication Title:	Comput. Geom.-Theory Appl.
Volume:	44
Number:	8
Page Range:	S. 385 - 399
Date:	2011
Publisher:	ELSEVIER SCIENCE BV
Place of Publication:	AMSTERDAM
ISSN:	0925-7721
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language ALGORITHM; PATHS Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/48875