Lecture Notes in Computer Science 8165Commenced Publication in 1973Founding and Former Series Editors:Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board

David Hutchison, UK

Josef Kittler, UK

Alfred Kobsa, USA

John C. Mitchell, USA

Oscar Nierstrasz, Switzerland

Bernhard Steffen, Germany

Demetri Terzopoulos, USA

Gerhard Weikum, Germany

Takeo Kanade, USA

Jon M. Kleinberg, USA

Friedemann Mattern, Switzerland

Moni Naor, Israel

C. Pandu Rangan, India

Madhu Sudan, USA

Doug Tygar, USA

Advanced Research in Computing and Software Science

Subline of Lectures Notes in Computer Science

Subline Series Editors

Giorgio Ausiello, University of Rome ‘La Sapienza’, Italy

Vladimiro Sassone, University of Southampton, UK

Subline Advisory Board

Susanne Albers, University of Freiburg, Germany

Benjamin C. Pierce, University of Pennsylvania, USA

Bernhard Steffen, University of Dortmund, Germany

Madhu Sudan, Microsoft Research, Cambridge, MA, USA

Deng Xiaotie, City University of Hong Kong

Jeannette M. Wing, Microsoft Research, Redmond, WA, USA

Andreas Brandstädt Klaus JansenRüdiger Reischuk (Eds.)

Graph-TheoreticConceptsin Computer Science

39th International Workshop, WG 2013Lübeck, Germany, June 19-21, 2013Revised Papers

13

Volume Editors

Andreas BrandstädtUniversity of Rostock, Institute of Computer ScienceAlbert-Einstein-Straße 22, 18059 Rostock, GermanyE-mail: ab@informatik.uni-rostock.de

Klaus JansenUniversity of Kiel, Department of Computer ScienceOlshausenstraße 40, 24098 Kiel, GermanyE-mail: kj@informatik.uni-kiel.de

Rüdiger ReischukUniversity of Lübeck, Institute of Theoretical Computer ScienceRatzeburger Allee 160, 23538 Lübeck, GermanyE-mail: reischuk@tcs.uni-luebeck.de

ISSN 0302-9743 e-ISSN 1611-3349ISBN 978-3-642-45042-6 e-ISBN 978-3-642-45043-3DOI 10.1007/978-3-642-45043-3Springer Heidelberg New York Dordrecht London

Library of Congress Control Number: 2013952713

CR Subject Classification (1998): G.2, F.2, I.2.8, E.1, I.3

LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues

© Springer-Verlag Berlin Heidelberg 2013This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting, reproduction on microfilms or in any other physical way, and transmission or informationstorage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodologynow known or hereafter developed. Exempted from this legal reservation are brief excerpts in connectionwith reviews or scholarly analysis or material supplied specifically for the purpose of being entered andexecuted on a computer system, for exclusive use by the purchaser of the work. Duplication of this publicationor parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location,in ist current version, and permission for use must always be obtained from Springer. Permissions for usemay be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecutionunder the respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoes not imply, even in the absence of a specific statement, that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date of publication,neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors oromissions that may be made. The publisher makes no warranty, express or implied, with respect to thematerial contained herein.

Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Preface

The 39th International Workshop on Graph-Theoretic Concepts in ComputerScience (WG 2013) took place in Lubeck, Germany, June 19–21, 2013.

The WG conference has a long tradition. Since 1975, it has taken place 22times in Germany, four times in The Netherlands, twice in Austria, the CzechRepublic, and France as well as once in Italy, Slovakia, Switzerland, Norway, theUK, Greece, and in Israel.

The WG conference aims to connect theory and practice by demonstratinghow graph-theoretic concepts can be applied to various areas of computer scienceand by extracting new graph-theoretic problems from applications. The goal isto present new research results and to identify and explore directions of futureresearch.

There were 61 submissions. Each submission was carefully reviewed by atleast four members of the Program Committee. The committee accepted 34papers to be presented at the workshop. The program also included three inspir-ing invited talks: Ola Svensson (EPFL Lausanne, Switzerland) presented “NewApproaches for Approximating TSP,” Berthold Vocking (RWTH Aachen, Ger-many) discussed the problem “Online Independent Set for Graphs with BoundedInductive Independence,” and Feodor F. Dragan (Kent State University, USA)gave a talk about “Tree-like Structures in Graphs: a Metric Point of View.”

We would like to thank the authors who submitted their papers, the speak-ers, the members of the Program Committee, and the external reviewers. Specialthanks to the local Organizing Committee; without their performance the con-ference could not have been such a success.

We are grateful to the Institute of Computer Science at the University of Ro-stock, the Institute of Computer Science of the Christian-Albrechts-Universitatzu Kiel, and the Institute of Theoretical Computer Science at the University ofLubeck.

August 2013 Andreas BrandstadtKlaus Jansen

Rudiger Reischuk

Organization

Program Committee

Andreas Brandstadt University of Rostock, GermanyArtur Czumaj University of Warwick, UKPinar Heggernes University of Bergen, NorwayJuraj Hromkovic ETH Zurich, SwitzerlandKlaus Jansen University of Kiel, GermanyJan Kratochvil Charles University, Czech RepublicVan Bang Le University of Rostock, GermanyBodo Manthey University of Twente, The NetherlandsDaniel Marx Hungarian Academy of Sciences, HungaryMonaldo Mastrolilli IDSIA Lugano, SwitzerlandErnst W. Mayr TU Munchen, GermanyHaiko Muller University of Leeds, UKRolf Niedermeier TU Berlin, GermanyChristophe Paul LIRMM Montpellier, FranceDieter Rautenbach University of Ulm, GermanyRudiger Reischuk University of Lubeck, GermanyHeiko Roglin University of Bonn, GermanyChristian Sohler TU Dortmund, GermanyIoan Todinca Universite d’Orleans, FranceDorothea Wagner University of Karlsruhe, Germany

Additional Reviewers

Barhum, KfirBaum, MoritzBelmonte, RemyBentz, CedricBerndt, SebastianBerry, AnneBlasius, ThomasBodlaender, Hans L.Boehme, ThomasBollig, BeateBonichon, NicolasBonomo, FlaviaBonsma, PaulBousquet, NicolasBrandes, Ulrik

Broersma, HajoBockenhauer, Hans-JoachimChang, Maw-ShangChapelle, MathieuChaplick, StevenChauve, CedricCheilaris, PanagiotisCrespelle, ChristopheDibbelt, JulianDidimo, WalterDoerr, CarolaDragan, FeodorDrechsler, RolfDriemel, AnneDvorak, Zdenek

VIII Organization

Ehsanfar, EbrahimElberfeld, MichaelEnglert, MatthiasErlebach, ThomasFabila-Monroy, RuyFarzad, BabakFeldmann, Andreas EmilFelsner, StefanFernau, HenningFigueiredo, CelinaFroese, VincentFuchs, FabianFulek, RadoslavGargano, LuisaGaspers, SergeGebauer, HeidiGille, MarcGolovach, PetrGoncalves, DanielGuo, JiongGurski, FrankHartmann, TanjaHartung, SeppHellweg, FrankHlineny, PetrHoefer, MartinHoeksma, RubenHuffner, FalkJansen, Bart M.P.Kaklamanis, ChristosKappes, AndreaKeller, LuciaKern, WalterKlavık, PavelKobourov, StephenKomm, DennisKomusiewicz, ChristianKosirova, IvanaKowaluk, MiroslawKratsch, DieterKratsch, StefanKrivosija, AmerKrug, SachaKunold, TimKohler, Ekkehard

Land, KatiLeveque, BenjaminLi, ZhentaoLiedloff, MathieuLimouzy, VincentLingas, AndrzejLiskiewicz, MaciejLokshtanov, DanielMaffray, FredericMatamala, MartınMchedlidze, TamaraMeister, DanielMertzios, GeorgeMilanic, MartinMunteanu, AlexanderNichterlein, AndreNiedermann, BenjaminNisse, NicolasOchem, PascalOtachi, YotaOum, Sang-IlPaulusma, DanielPeng, Sheng-LungPilipczuk, MarcinPilipczuk, Micha�lPinkau, ChrisProskurowski, AndrzejProtti, FabioPrutkin, RomanRafiey, ArashRutter, IgnazSalazar, GelasioSau, IgnasiSchiermeyer, IngoSchmidt, MelanieSchuster, MartinSchweitzer, PascalSchwiegelshohn, ChrisSerna, MariaShah, ChintanSmula, JasminSorge, ManuelSprock, AndreasStamoulis, GeorgiosSteffen, Bjorn

Organization IX

Steiner, GeorgeStockhusen, ChristophStrasser, BenSuchy, OndrejTaeubig, HanjoTantau, TillThilikos, DimitriosTholey, TorstenThomborson, ClarkToman, StefanTorok, L’ubomırvan’t Hof, Pimvan Bevern, Rene

van der Zwaan, RubenVillanger, YngveWahlstrom, MagnusWalczak, BartoszWeihmann, JeremiasWeller, MathiasWestermann, MatthiasWhidden, ChrisWilson, SamuelWitt, OliverWollan, PaulWood, DavidZemmari, Akka

Abstracts

Tree-Like Structures in Graphs:

A Metric Point of View�

Feodor F. Dragan

Department of Computer Science, Kent State University, Kent, OH 44242, USA

dragan@cs.kent.edu

Abstract. Recent empirical and theoretical work has suggested thatmany real-life complex networks and graphs arising in Internet applica-tions, in biological and social sciences, in chemistry and physics havetree-like structures from a metric point of view. A number of graphparameters trying to capture this phenomenon and to measure thesetree-like structures were proposed; most notable ones being the tree-stretch, tree-distortion, tree-length, tree-breadth, Gromov’s hyperbolicityof a graph, and cluster-diameter and cluster-radius in a layering partitionof a graph. If such a parameter is bounded by a constant on graphs thenmany optimization problems can be efficiently solved or approximatedfor such graphs. We discuss these parameters and recently established re-lationships between them for unweighted and undirected graphs; it turnsout that all these parameters are at most constant or logarithmic factorsapart from each other. We give inequalities describing their relationshipsand discuss consequences for some optimization problems.

* Dedicated to Professor Andreas Brandstadt, on the occasion of his 65th birthday.

Overview of New Approaches

for Approximating TSP

Ola Svensson

Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland

ola.svensson@epfl.ch

Abstract. In this extended abstract, we survey some of the recentresults on approximating the traveling salesman problem on graphicmetrics.

We start by briefly explaining the algorithm of Oveis Gharan et al. [1]that has strong similarities to Christofides’ famous 3/2-approximationalgorithm. We then explain the main ideas behind an alternative ap-proach introduced by Momke and the author [2]. The new ingredientin our approach is that it allows for the removal of certain edges whilesimultaneously yielding a connected, Eulerian graph, which in turn leadsto a decreased cost. We also overview the exciting developments for TSPon graphic metrics that rapidly followed: an improved analysis of ouralgorithm by Mucha [3] yielding an approximation guarantee of 1.44,and the recent developments by Sebo and Vygen [3] who gave a 1.4-approximation algorithm.

Finally, we point out some interesting open problems where our tech-niques currently fall short of applying to more general metrics.

Online Independent Set for Graphs

with Bounded Inductive Independence

Berthold Vocking

Department of Computer ScienceRWTH Aachen University

voecking@cs.rwth-aachen.de

In this invited talk, we present techniques and restuls from a joint work withOliver Gobel, Martin Hoefer, Thomas Kesselheim, and Thomas Schleiden [1]. Westudy online algorithms for maximum (weight) independent set on graph classeswith bounded inductive independence number like interval and disk graphs withapplications to, e.g., task scheduling and spectrum allocation. In the consideredonline setting, it is assumed that nodes of an unknown graph arrive one by oneover time. An online algorithm has to decide whether an arriving node should beincluded into the independent set. We explain that this natural and practicallyrelevant online problem cannot be studied in a meaningful way within a classicalcompetitive analysis as the competitive ratio on worst-case input sequences islower bounded by Ω(n). This devastating lower bound holds even for randomizedalgorithms on unweighted interval graphs and, hence, for the most restrictedgraph class under consideration.

As a worst-case analysis is pointless, we study online independent set in astochastic analysis. Instead of focussing on a particular stochastic input model,we present a generic sampling approach that enables us to devise online al-gorithms achieving performance guarantees for a variety of input models. Inparticular, our analysis covers stochastic input models like the secretary model,in which an adversarial graph is presented in random order, and the prophet-inequality model, in which a randomly generated graph is presented in adversar-ial order. Our sampling approach bridges thus between stochastic input modelsof quite different nature. In addition, we show that the same performance guaran-tees can be obtained for a period-based input model that is inspired by practicaladmission control applications.

Using the graph sampling approach, we devise an online algorithm for theunweighted independent set problem with competitive ratio O(ρ2) for graphswith inductive independence number ρ. This way, we achieve competitive ratioO(1) for independent set on interval and disk graphs. For weighted independentset, we obtain a competitive ratio of O

(ρ2 logn

)where n denotes the number

of nodes. In addition, we show that this bound is almost best possible for interval

XVI B. Vocking

and disk graphs. In particular, we prove a lower bound on the competitive ratiofor weighted independent set on interval graphs of order Ω

(log n/ log2 logn

).

Reference

1. Oliver Gobel, Martin Hoefer, Thomas Kesselheim, Thomas Schleiden, BertholdVocking. Online Independent Set Beyond the Worst-Case: Secretaries, Prophets,and Periods. Technical Report. CoRR abs/1307.3192, 2013.

Table of Contents

Tree-Like Structures in Graphs: A Metric Point of View . . . . . . . . . . . . . . 1Feodor F. Dragan

Overview of New Approaches for Approximating TSP . . . . . . . . . . . . . . . . 5Ola Svensson

Linear Rank-Width and Linear Clique-Width of Trees . . . . . . . . . . . . . . . . 12Isolde Adler and Mamadou Moustapha Kante

Threshold-Coloring and Unit-Cube Contact Representation ofGraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Md. Jawaherul Alam, Steven Chaplick, Gasper Fijavz,Michael Kaufmann, Stephen G. Kobourov, and Sergey Pupyrev

Rolling Upward Planarity Testing of Strongly Connected Graphs . . . . . . . 38Christopher Auer, Christian Bachmaier,Franz J. Brandenburg, and Kathrin Hanauer

Towards a Provably Resilient Scheme for Graph-BasedWatermarking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Lucila Maria Souza Bento, Davidson Boccardo,Raphael Carlos Santos Machado,Vinıcius Gusmao Pereira de Sa, and Jayme Luiz Szwarcfiter

The Normal Graph Conjecture for Classes of Sparse Graphs . . . . . . . . . . . 64Anne Berry and Annegret Wagler

On the Parameterized Complexity of Computing Graph Bisections . . . . . 76Rene van Bevern, Andreas Emil Feldmann, Manuel Sorge, andOndrej Suchy

Fixed-Parameter Tractability and Characterizations of Small SpecialTreewidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Hans L. Bodlaender, Stefan Kratsch, and Vincent J.C. Kreuzen

The θ5-Graph is a Spanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Prosenjit Bose, Pat Morin, Andre van Renssen, andSander Verdonschot

Graphs of Edge-Intersecting Non-splitting Paths in a Tree: TowardsHole Representations (Extended Abstract) . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Arman Boyacı, Tınaz Ekim, Mordechai Shalom, and Shmuel Zaks

XVIII Table of Contents

Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Hajo Broersma, Jirı Fiala, Petr A. Golovach, Tomas Kaiser,Daniel Paulusma, and Andrzej Proskurowski

Equilateral L-Contact Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139Steven Chaplick, Stephen G. Kobourov, and Torsten Ueckerdt

Parameterized and Approximation Algorithms for the MAF Problemin Multifurcating Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Jianer Chen, Jia-Hao Fan, and Sing-Hoi Sze

Linear Separation of Total Dominating Sets in Graphs . . . . . . . . . . . . . . . . 165Nina Chiarelli and Martin Milanic

Sparse Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Manfred Cochefert, Jean-Francois Couturier, Petr A. Golovach,Dieter Kratsch, and Daniel Paulusma

Completing Colored Graphs to Meet a Target Property . . . . . . . . . . . . . . . 189Kathryn Cook, Elaine M. Eschen, R. Sritharan, and Xiaoqiang Wang

Colouring of Graphs with Ramsey-Type Forbidden Subgraphs . . . . . . . . . 201Konrad K. Dabrowski, Petr A. Golovach, and Daniel Paulusma

Lower and Upper Bounds for Long Induced Paths in 3-ConnectedPlanar Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Emilio Di Giacomo, Giuseppe Liotta, and Tamara Mchedlidze

Computing Minimum Cycle Bases in Weighted Partial 2-Trees inLinear Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Carola Doerr, G. Ramakrishna, and Jens M. Schmidt

Thickness and Colorability of Geometric Graphs . . . . . . . . . . . . . . . . . . . . . 237Stephane Durocher, Ellen Gethner, and Debajyoti Mondal

The Same Upper Bound for Both: The 2-Page and the RectilinearCrossing Numbers of the n-Cube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

Luerbio Faria, Celina M.H. de Figueiredo, R. Bruce Richter, andImrich Vrt’o

FPT Is Characterized by Useful Obstruction Sets . . . . . . . . . . . . . . . . . . . . 261Michael R. Fellows and Bart M.P. Jansen

Excluding Graphs as Immersions in Surface Embedded Graphs . . . . . . . . 274Archontia C. Giannopoulou, Marcin Kaminski, andDimitrios M. Thilikos

OBDD-Based Representation of Interval Graphs . . . . . . . . . . . . . . . . . . . . . 286Marc Gille

Table of Contents XIX

Tight Upper Bounds for Minimum Feedback Arc Sets of RegularGraphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298

Kathrin Hanauer, Franz J. Brandenburg, and Christopher Auer

A Linear-Time Kernelization for the Rooted k -Leaf OutbranchingProblem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

Frank Kammer

On Retracts, Absolute Retracts, and Folds in Cographs . . . . . . . . . . . . . . . 321Ton Kloks and Yue-Li Wang

Coloring Triangle-Free Rectangular Frame Intersection Graphs withO(log log n) Colors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

Tomasz Krawczyk, Arkadiusz Pawlik, and Bartosz Walczak

On Finding Tucker Submatrices and Lekkerkerker-Boland Subgraphs . . . 345Nathan Lindzey and Ross M. McConnell

Certifying 3-Edge-Connectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358Kurt Mehlhorn, Adrian Neumann, and Jens M. Schmidt

Parameterized Algorithms for Max Colorable Induced Subgraph

Problem on Perfect Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370Neeldhara Misra, Fahad Panolan, Ashutosh Rai,Venkatesh Raman, and Saket Saurabh

Characterizing and Computing the Structure of Clique Intersections inStrongly Chordal Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

Ragnar Nevries and Christian Rosenke

Beyond Knights and Knaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394Christine T. Cheng, Andrew McConvey, Drew Onderko,Nathaniel Shar, and Charles Tomlinson

Drawing Graphs with Few Arcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406Andre Schulz

Connecting Terminals and 2-Disjoint Connected Subgraphs . . . . . . . . . . . . 418Jan Arne Telle and Yngve Villanger

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429