Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges

J. Joseph Fowler; Michael Jünger; Stephen Kobourov; Michael Schulz

doi:10.1007/978-3-540-92248-3_14

Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges

J. Joseph Fowler, Michael Jünger, Stephen Kobourov, Michael Schulz

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

9 Scopus citations

Abstract

A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K ₅ or K _3,3. 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 efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.

Original language	English (US)
Title of host publication	Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers
Pages	146-158
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-540-92248-3_14
State	Published - 2008
Event	34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 - Durham, United Kingdom Duration: Jun 30 2008 → Jul 2 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5344 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008
Country	United Kingdom
City	Durham
Period	6/30/08 → 7/2/08

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-92248-3_14

Fingerprint Dive into the research topics of 'Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges'. Together they form a unique fingerprint.

Cite this

Fowler, J. J., Jünger, M., Kobourov, S., & Schulz, M. (2008). Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges. In Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers (pp. 146-158). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5344 LNCS). https://doi.org/10.1007/978-3-540-92248-3_14

Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges. / Fowler, J. Joseph; Jünger, Michael; Kobourov, Stephen; Schulz, Michael.

Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers. 2008. p. 146-158 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5344 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Fowler, JJ, Jünger, M, Kobourov, S & Schulz, M 2008, Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges. in Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5344 LNCS, pp. 146-158, 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008, Durham, United Kingdom, 6/30/08. https://doi.org/10.1007/978-3-540-92248-3_14

Fowler JJ, Jünger M, Kobourov S, Schulz M. Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges. In Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers. 2008. p. 146-158. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-92248-3_14

Fowler, J. Joseph ; Jünger, Michael ; Kobourov, Stephen ; Schulz, Michael. / Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges. Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers. 2008. pp. 146-158 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{0c7508bd401f42e8a54d5e648c43bcbd,

title = "Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges",

abstract = "A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K 5 or K 3,3. 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 efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.",

author = "Fowler, {J. Joseph} and Michael J{\"u}nger and Stephen Kobourov and Michael Schulz",

note = "Copyright: Copyright 2009 Elsevier B.V., All rights reserved.; 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008 ; Conference date: 30-06-2008 Through 02-07-2008",

year = "2008",

doi = "10.1007/978-3-540-92248-3_14",

language = "English (US)",

isbn = "3540922474",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "146--158",

booktitle = "Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers",

}

TY - GEN

T1 - Characterizations of restricted pairs of planar graphs allowing simultaneous embedding with fixed edges

AU - Fowler, J. Joseph

AU - Jünger, Michael

AU - Kobourov, Stephen

AU - Schulz, Michael

PY - 2008

Y1 - 2008

N2 - A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K 5 or K 3,3. 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 efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.

AB - A set of planar graphs share a simultaneous embedding if they can be drawn on the same vertex set V in the Euclidean plane without crossings between edges of the same graph. Fixed edges are common edges between graphs that share the same simple curve in the simultaneous drawing. Determining in polynomial time which pairs of graphs share a simultaneous embedding with fixed edges (SEFE) has been open. We give a necessary and sufficient condition for whether a SEFE exists for pairs of graphs whose union is homeomorphic to K 5 or K 3,3. 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 efficient algorithms to compute a SEFE. Finally, we provide a linear-time decision algorithm for deciding whether a pair of biconnected outerplanar graphs has a SEFE.

UR - http://www.scopus.com/inward/record.url?scp=58349101647&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58349101647&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-92248-3_14

DO - 10.1007/978-3-540-92248-3_14

M3 - Conference contribution

AN - SCOPUS:58349101647

SN - 3540922474

SN - 9783540922476

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 146

EP - 158

BT - Graph-Theoretic Concepts in Computer Science - 34th International Workshop, WG 2008, Revised Papers

T2 - 34th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2008

Y2 - 30 June 2008 through 2 July 2008

ER -