Thirty Essays on Geometric Graph Theory PDF
Preview Thirty Essays on Geometric Graph Theory
János Pach Editor Thirty Essays on Geometric Graph Theory Thirty Essays on Geometric Graph Theory Ja´nos Pach Editor Thirty Essays on Geometric Graph Theory 123 Editor Ja´nosPach Alfre´dRe´nyiInstituteofMathematics HungarianAcademyofSciences Budapest,Hungary and ChairofCombinatorialGeometry E´colePolytechniqueFe´de´raledeLausanne Lausanne,Switzerland ISBN978-1-4614-0109-4 ISBN978-1-4614-0110-0 (eBook) DOI10.1007/978-1-4614-0110-0 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2012952159 MathematicsSubjectClassification:05-06,05C62,68R10,05C35,52C10 ©SpringerScience+BusinessMediaNewYork2013,Correctedat2ndprinting,2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Cover image: Redrawn image of Erhard Scho¨n’s “Fu¨nf Figuren in einem Geba¨ude,” published in UnnderweissungderProportzion(Nu¨rnberg,1538). Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Contents Introduction ...................................................................... 1 Ja´nosPach TheRectilinearCrossingNumberofK :Closingin(orAreWe?)......... 5 n BernardoM.A´brego,SilviaFerna´ndez-Merchant,andGelasioSalazar TheMaximumNumberofTangenciesAmongConvexRegions withaTriangle-FreeIntersectionGraph...................................... 19 EyalAckerman BlockingColoredPointSets .................................................... 31 GregAloupis,BradBallinger,Se´bastienCollette,StefanLangerman, AttilaPo´r,andDavidR.Wood ConstrainedTri-ConnectedPlanarStraightLineGraphs .................. 49 MarwanAl-Jubeh,GillBarequet,MashhoodIshaque, DianeL.Souvaine,CsabaD.To´th,andAndrewWinslow TopologicalHypergraphs........................................................ 71 SaritBuzaglo,RomPinchasi,andGu¨nterRote OnEdge-DisjointEmptyTrianglesofPointSets............................. 83 JavierCano,LuisF.Barba,ToshinoriSakai,andJorgeUrrutia UniversalSetsforStraight-LineEmbeddingsofBicoloredGraphs........ 101 Josef Cibulka, Jan Kyncˇl, Viola Me´sza´ros, Rudolf Stolaˇr, andPavelValtr DrawingTrees,OuterplanarGraphs,Series-ParallelGraphs, andPlanarGraphsinaSmallArea............................................ 121 GiuseppeDiBattistaandFabrizioFrati v vi Contents TheCrossing-AngleResolutioninGraphDrawing.......................... 167 WalterDidimoandGiuseppeLiotta MoverProblems.................................................................. 185 AdrianDumitrescu Rectangle and Square Representations ofPlanarGraphs................................................................. 213 StefanFelsner Convex Obstacle Numbers of Outerplanar Graphs andBipartitePermutationGraphs............................................. 249 RadoslavFulek,NoushinSaeedi,andDenizSarıo¨z Hanani–Tutte,MonotoneDrawings,andLevel-Planarity................... 263 Radoslav Fulek, Michael J. Pelsmajer, Marcus Schaefer, andDanielSˇtefankovicˇ OnDisjointCrossingFamiliesinGeometricGraphs ........................ 289 RadoslavFulekandAndrewSuk CountingPlaneGraphs:FlippabilityandItsApplications.................. 303 MichaelHoffmann,Andre´ Schulz,MichaSharir,AdamSheffer, CsabaD.To´th,andEmoWelzl PlaneGeometricGraphAugmentation:AGenericPerspective............ 327 FerranHurtadoandCsabaD.To´th DiscreteGeometryonRedandBluePointsinthePlaneLattice ........... 355 MikioKanoandKazuhiroSuzuki Ramsey-TypeProblemsforGeometricGraphs .............................. 371 GyulaKa´rolyi Blockers for Noncrossing Spanning Trees in Complete GeometricGraphs ............................................................... 383 Chaya Keller, Micha A. Perles, Eduardo Rivera-Campo, andVirginiaUrrutia-Galicia ColoringCleanandK -FreeCircleGraphs................................... 399 4 AlexandrV.KostochkaandKevinG.Milans Counting Large Distances in Convex Polygons: AComputationalApproach..................................................... 415 FilipMoric´andDavidPritchard ColoringDistanceGraphsandGraphsofDiameters........................ 429 AndreiM.Raigorodskii RealizabilityofGraphsandLinkages ......................................... 461 MarcusSchaefer Contents vii EquilateralSetsin(cid:2)d ............................................................ 483 p CliffordSmyth ANoteonGeometric3-Hypergraphs.......................................... 489 AndrewSuk FavoriteDistancesinHighDimensions........................................ 499 KonradJ.Swanepoel IntersectionPatternsofConvexSetsviaSimplicialComplexes: ASurvey........................................................................... 521 MartinTancer ConstructionofLocallyPlaneGraphswithManyEdges ................... 541 Ga´borTardos ABetterBoundforthePair-CrossingNumber............................... 563 Ge´zaTo´th Minors,Embeddability,andExtremalProblemsforHypergraphs........ 569 UliWagner Contributors BernardoM.A´brego DepartmentofMathematics,CaliforniaStateUniversityat Northridge,LosAngeles,CA,USA Eyal Ackerman Department of Mathematics, Physics, and Computer Science, UniversityofHaifaatOranim,Tivon,Israel MarwanAl-Jubeh DepartmentofComputerScience,TuftsUniversity,Medford, MA,USA Greg Aloupis De´partementd’Informatique,Universite´ Libre de Bruxelles, Brus- sels,Belgium Brad Ballinger Departmentof Mathematics, HumboldtState University, Arcata, CA,USA Luis F. Barba Instituto de Matema´ticas, Universidad Nacional Auto´noma de Me´xico,D.F.,Mexico GillBarequet DepartmentofComputerScience,Technion,Haifa,Israel DepartmentofComputerScience,TuftsUniversity,Medford,MA,USA Giuseppe Di Battista Dipartimento di Informatica e Automazione, Roma Tre University,Rome,Italy SaritBuzaglo MathematicsDepartment,Technion-IsraelInstituteofTechnology, Haifa,Israel Javier Cano Instituto de Matema´ticas, Universidad Nacional Auto´noma de Me´xico,D.F.,Mexico Josef Cibulka Department of Applied Mathematics, Charles University, Prague, CzechRepublic Se´bastien Collette De´partement d’Informatique, Universite´ Libre de Bruxelles, Brussels,Belgium ix
The list of books you might like
