TY - GEN

T1 - The QuaSEFE Problem

AU - Angelini, Patrizio

AU - Förster, Henry

AU - Hoffmann, Michael

AU - Kaufmann, Michael

AU - Kobourov, Stephen

AU - Liotta, Giuseppe

AU - Patrignani, Maurizio

N1 - Funding Information:
Work started at Dagstuhl Seminar 19092, ?Beyond-Planar Graphs: Combinatorics, Models and Algorithms?. Research supported by MIUR Project ?MODE? under PRIN 20157EFM5C, by MIUR Project ?AHeAD? under PRIN 20174LF3T8, by Roma Tre University Azione 4 Project ?GeoView?, by DFG grant Ka812/17-1, by NSF under grants CCF-1740858 and CCF-1712119, and by SNSF Project 200021E-171681.

PY - 2019

Y1 - 2019

N2 - We initiate the study of Simultaneous Graph Embedding with Fixed Edges in the beyond planarity framework. In the QuaSEFE problem, we allow edge crossings, as long as each graph individually is drawn quasiplanar, that is, no three edges pairwise cross. We show that a triple consisting of two planar graphs and a tree admit a QuaSEFE. This result also implies that a pair consisting of a 1-planar graph and a planar graph admits a QuaSEFE. We show several other positive results for triples of planar graphs, in which certain structural properties for their common subgraphs are fulfilled. For the case in which simplicity is also required, we give a triple consisting of two quasiplanar graphs and a star that does not admit a QuaSEFE. Moreover, in contrast to the planar SEFE problem, we show that it is not always possible to obtain a QuaSEFE for two matchings if the quasiplanar drawing of one matching is fixed.

AB - We initiate the study of Simultaneous Graph Embedding with Fixed Edges in the beyond planarity framework. In the QuaSEFE problem, we allow edge crossings, as long as each graph individually is drawn quasiplanar, that is, no three edges pairwise cross. We show that a triple consisting of two planar graphs and a tree admit a QuaSEFE. This result also implies that a pair consisting of a 1-planar graph and a planar graph admits a QuaSEFE. We show several other positive results for triples of planar graphs, in which certain structural properties for their common subgraphs are fulfilled. For the case in which simplicity is also required, we give a triple consisting of two quasiplanar graphs and a star that does not admit a QuaSEFE. Moreover, in contrast to the planar SEFE problem, we show that it is not always possible to obtain a QuaSEFE for two matchings if the quasiplanar drawing of one matching is fixed.

KW - Quasiplanar

KW - SEFE

KW - Simultaneous graph drawing

UR - http://www.scopus.com/inward/record.url?scp=85076910884&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076910884&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-35802-0_21

DO - 10.1007/978-3-030-35802-0_21

M3 - Conference contribution

AN - SCOPUS:85076910884

SN - 9783030358013

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

SP - 268

EP - 275

BT - Graph Drawing and Network Visualization - 27th International Symposium, GD 2019, Proceedings

A2 - Archambault, Daniel

A2 - Tóth, Csaba D.

PB - Springer

T2 - 27th International Symposium on Graph Drawing and Network Visualization, GD 2019

Y2 - 17 September 2019 through 20 September 2019

ER -