Drawing Simultaneously Embedded Graphs with Few Bends-Reference-Cited by-同舟云学术

Drawing Simultaneously Embedded Graphs with Few Bends

Published:2023-05-09 Issue:07 Volume:34 Page:807-824
ISSN:0129-0541
Container-title:International Journal of Foundations of Computer Science
language:en
Short-container-title:Int. J. Found. Comput. Sci.

Author:

Grilli Luca¹,Hong Seok-Hee²,Kratochvíl Jan³,Rutter Ignaz⁴

Affiliation:

1. Dipartimento di Ingegneria, Università degli Studi di Perugia, Via G. Duranti 93, 06125 Perugia, Italia

2. School of Computer Science, University of Sydney, Camperdown NSW 2006, Australia

3. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, Prague CZ-11800, Czechia

4. Faculty of Computer Science and Mathematics, University of Passau, Innstraße 33, 94032 Passau, Germany

Abstract

We study the problem of drawing simultaneously embedded graphs with few bends. We show that for any simultaneous embedding with fixed edges (SEFE) of two graphs, there exists a corresponding drawing realizing this embedding such that common edges are drawn as straight-line segments and each exclusive edge has a constant number of bends. If the common graph is biconnected and induced, a straight-line drawing exists. This yields the first efficient testing algorithm for simultaneous geometric embedding (SGE) for a non-trivial class of graphs.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Computer Science (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129054123420017

Reference25 articles.

1. Testing the simultaneous embeddability of two graphs whose intersection is a biconnected or a connected graph

2. On a Tree and a Path with no Geometric Simultaneous Embedding

3. LIPIcs;Bläsius T.,2021

4. LNCS;Bläsius T.,2013