Combinatorics, Graph Theory and Computing: SEICCGTC 2020, Boca Raton, USA, March 9–13 PDF
Preview Combinatorics, Graph Theory and Computing: SEICCGTC 2020, Boca Raton, USA, March 9–13
Springer Proceedings in Mathematics & Statistics Frederick Hoffman Editor Combinatorics, Graph Theory and Computing SEICCGTC 2020, Boca Raton, USA, March 9–13 Springer Proceedings in Mathematics & Statistics Volume 388 This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics,includingdatascience,operationsresearchandoptimization.Inaddition to an overall evaluation of the interest, scientific quality, and timeliness of each proposalatthehandsofthepublisher,individualcontributionsareallrefereedtothe highqualitystandardsofleadingjournalsinthefield.Thus,thisseriesprovidesthe researchcommunitywithwell-edited,authoritativereportsondevelopmentsinthe mostexcitingareasofmathematicalandstatisticalresearchtoday. Frederick Hoffman Editor Combinatorics, Graph Theory and Computing SEICCGTC 2020, Boca Raton, USA, March 9–13 Editor FrederickHoffman DepartmentofMathematicalSciences FloridaAtlanticUniversity BocaRaton,FL,USA ISSN 2194-1009 ISSN 2194-1017 (electronic) SpringerProceedingsinMathematics&Statistics ISBN 978-3-031-05374-0 ISBN 978-3-031-05375-7 (eBook) https://doi.org/10.1007/978-3-031-05375-7 MathematicsSubjectClassification:05-XX,05-06,05Cxx,12-XX,12-06,68Rxx,68R05,52-XX,52-06 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2022 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface I The Southeastern International Conference on Combinatorics, Graph Theory, and Computing (SEICCGTC) is an international meeting of mathematical scientists, heldannuallyinMarch,duringSpringBreakatFloridaAtlanticUniversity(FAU) inBocaRaton,Florida.Theconferenceincludesaprogramwithplenarylecturesby invitedspeakers,aswellassessionsofcontributedpaperseachday.Inaddition,two or three invitational special sessions are offered each year. A valuable part of the conferenceistheopportunityaffordedforinformalconversationsaboutthemethods participantsemployintheirprofessionalworkinbusiness,industry,andgovernment andabouttheircurrentresearch. The51stmeetingwasheldinthenewlyrenovatedStudentUnionbuildingatFAU, March9–13,2020.Fivedistinguishedresearchers,atvariousstagesoftheircareers, accepted invitations to attend as plenary speakers at this year’s 51st SEICCGTC: PierreBaldi,UniversityofCalifornia,Irvine,USA;PavolHell,SimonFraserUniver- sity,Canada;PatriciaHersh,UniversityofOregon,USA;PanosM.Pardalos,Univer- sity of Florida, USA; and Kai-Uwe Schmidt, Paderborn University, Germany. Dr. Pardaloshadtocancelhistalkatthelastmoment,duetoillnessandthepandemic. Eachoftheotherplenaryspeakersgavetwotalks.Thereweretwospecialsessions thisyear,oneonResearchbyWomeninGraphTheoryanditsApplications,orga- nized by Leslie Hogben, and one on Extremal Graph Theory, organized by Neal Bushaw.Bothwerewellattendedandwellreceived.Plenaryandcontributedtalks coveredawidevarietyoftopicsincluding:newtoolsforcountingandlinearprogram- ming,usingtopologicalmethods;graphhomomorphism;graphswithloops;highly non-linearfunctionsandcodingtheory;associationschemes;deeplearningandits mathematicalfoundations;extremalgraphtheory;posets;latinsquares;combinato- rialgames;coloring,connectivity,domination,labeling,andpartitioningofgraphs; alongwithassociatedalgorithmsandapplications. Thecoronaviruspandemicof2020createdsomedifficultiesforourconference. Oneplenaryspeakercouldnotattend,andweexperienced20cancellationsduetothe virusoutbreak.Severalparticipantshadtheirreturntravelplansdisrupted;afewwere quiteworriedforadayortwo.TheFAUDepartmentofMathematicalScienceshosted approximately150conferenceparticipantsandguests,markinganothersuccessful v vi PrefaceI meetingoftheSEICCGTC!Forthemostpart,the51stmeetingoftheSEICCGTC wasagreatsuccessandconferenceparticipantsexpressedtheirapprovaloftheoverall qualityofspeakersandprogramsandthecontinuousimprovementsinthetechnology provided.Wehavecausetocelebrate! OnTuesday,March10,2020,wecelebratedthepublicationofthecommemorative bookentitled,“50YearsofCombinatorics,GraphtheoryandComputing,”published byCRC/Taylor&Francis.Twenty-ninepastplenaryspeakersandpastconference participants contributed 21 chapters for the book, edited by Fan Chung, Ronald Graham, Ronald Mullin, Frederick Hoffman, Douglas West and Leslie Hogben. The Institute of Combinatorics and its Applications held its annual meeting on Wednesday,March11. TheconferencealsofeaturedanoutdoorreceptionMondayeveningontheLive Oak Pavilion Patio, a sumptuous beachfront banquet Wednesday evening at the DelraySandsResort,aswellanexcursionThursdayafternoontotheFlaglerMuseum in Palm Beach, followed by an informal reception Thursday evening at the brand newSchmidtFamilyComplex.Thesocialprogramwascappedoffbyawonderful Survivors’PartyFridayevening,hostedbyAaronMeyerowitzandAndreaSchuver attheirhome! This year, we took another step toward elevating the quality of the conference, by agreeing to publish our conference proceedings with Springer Nature, in their PROMSseriesofhardbackconferenceproceedings.Thepurposeistomoreeffec- tivelyandefficientlycontinuetodisseminateimportantadvancesintherepresented disciplines and to ensure that the conference continues to promote better under- standingoftherolesofmodernappliedmathematics,combinatoricsandcomputer science;demonstratethecontributionofeachdisciplinetotheothers;anddecrease gaps between the fields, as it did through fifty years of publishing in the journal, CongressusNumerantium. The conference was supported by the Department chair and staff, with tech- nical support by Andrew Gultz. Outside support came from the National Security Agency,SpringerNature,CRCPress/Taylor&Francis,Algorithms,andTheInstitute of Combinatorics and its Applications. Conference coordination and organization wassuperblyprovidedbyDr.MariaProvost. I gratefully acknowledge the support and assistance of Sara Heuss Holliday, RichardLow,ZviRosen,FarhadShahrokhi,andJohnWiermaninthecompilation andreviewingoftheseProceedings.Wealsothankallourreferees. BocaRaton,USA FrederickHoffman Preface II Ratio balancing numbers, introduced here by Jeremy Bartz and his coauthors, are a generalization of balancing numbers, a concept from number theory involving triangularnumbers.Theauthorsdefinetheconceptandpresentexamples,existence results,andconjectures. BohanQuandStephenJ.Curranshowthatthenumberβ=(bb−1−1)/(b−1)2, whereb≥3,hasseveralinterestingmultiplicativeproperties.Inthebasebnumber system,β =(123···(b−4)(b−3)(b−1)) .Theyshowthatthedigitsofthenumber b Kβ,forintegersK suchthat1≤K ≤(b−1)2,asanumberinthebasebnumber systemcan begenerated fromanarithmeticsequence reduced modulo b −1with anappropriateadjustment. DennisDavenportandhiscoauthorsreportonrecentresultsoftheirresearchgroup onRiordanarrays.TheygeneralizeaknownrowconstructionofRiordanarraysto aresultonthedeterminationofdoubleRiordanarrays. TimothyMyersconstructstheCliffordgraphalgebraforanywindmillgraphW(r, m),whichconsistsofmcopiesofthecompletegraphK adjoinedatonecommon r vertex; and for any Dutch windmill graph Dm which consists of m copies of the r r-cyclegraphC adjoinedatonecommonvertex.Hethenappliestheconstruction r to give a new proof that these graphs, which possess the friendship property, are preciselythefriendshipgraphs. PaulPeartandFrancoisRamarosonconstructandfindthevaluesforcertainchar- actersumsinvolvingquadraticcharacters.Themethodisnewandemployselliptic curves.Detailedproofsareprovided. In work that originated in an REU at Illinois State University, Joel Jeffries and hiscoauthorsinvestigateamultigraphGwiththeunderlyingstructureofa4-cycle whereeachedgemultiplicityintheset{1,2,3,4}isrepresented.Theyrefertoeach ofthethreesuchmultigraphsasaStanton4-cycle.ForeachsuchG,theyconsiderλ suchthatthereexistsaG-decompositionofλK . n BrigitteServatiusconsidersthek-planematroid,whichisamatroidontheedge set,I,ofabipartitegraph,H=(A,B;I),definedbyacountingcondition.Sheshows that2k-connectivityofH impliesthatI isaspanningsetforthek-planematroidon vii viii PrefaceII the edge set of the complete bipartite graph on (A, B). For k = 2 she explains the connectionstorigidityintheplaneandtoconjecturesofWhiteley. FarhadShahrokhiderivesanupperboundonthetracefunctionofahypergraphH andgivessomeapplications.Forinstance,anewupperboundfortheVCdimension of H, or vc(H), follows as a consequence and can be used to compute vc(H) in polynomialtimeprovidedthatH hasboundeddegeneracy.Thiswasnotpreviously known, and improves computing time in some cases. Another consequence is a generallowerboundonthedistinguishingtransversalnumberofHthatgivesriseto applicationsindominationtheoryofgraphs. SarahHeussHollidaycontinuesworkonaquestionraisedin2017byHedetniemi: ForwhichgraphsGdoestheindexedfamilyofopenneighborhoodshaveasystem of distinct representatives? In earlier work with collaborators, that question was answered,andnecessaryconditionsandassociatedparameterswereexplored.Haenel andJohnsonlookedoverlongestpathsandcycles.Theworkherefurthergeneralizes anddeepenstheirexaminations. AtifAbueidaandKennethRobleeexamineharmoniouslabelingsofstarliketrees. It has been shown using cyclic groups that the disjoint union of an odd cycle on s verticesandstarliketreeswiththecentralvertexadjacenttosomeeventmanys-paths is harmonious. They consider the disjoint union of an odd cycle with at least two starlike trees with new notions of harmonious labelings to accommodate the case where|V|>|E|. AmeancoloringofaconnectedgraphGoforder3ormoreisanedgecoloringof Gwithpositiveintegerssuchthatthemeanofthecolorsoftheedgesincidentwith everyvertexisaninteger.Theassociatedcolorofavertexisitschromaticmean.If distinctverticeshavedistinctchromaticmeans,thentheedgecoloringisarainbow mean coloring of G. In their paper, Ebrahim Salehi and his coauthors investigate rainbowmeancoloringsoftrees. Peg solitaire is a game in which pegs are placed in every hole but one, and the playerjumpsoverpegstoremovethem.In2011,thisgamewasgeneralizedtographs. Here,RobertA.BeelerandAaronD.Grayexaminegraphsinwhichanysingleedge addition changes solvability. They provide necessary and sufficient conditions for solvabilityforacertainfamily.Theyshowthatinfinitesubsetsofthisfamilyareedge criticalanddeterminethemaximumnumberofpegsthatcanbeleftonthisfamily withtheconditionthatajumpismadewheneverpossible.Finally,theygivealistof graphsoneightverticesthatareedgecritical. Asetofvertices,S,inastronglyconnecteddigraphD,issplitdominatingprovided it is: (1) dominating and (2) D − S is trivial or not strongly connected. The split domination number is the minimum cardinality of a split dominating set for that digraph.SarahMerzandhercoauthorsshowthatforanyk-regulartournament,the split domination number is at least (2k+3)/3 and this bound is tight. They explore propertiesofregulartournamentswithsplitdominationnumberequaltothelower bound,includingsufficientconditionsfor{1}-extendability. DavidR.Prierandhiscoauthorsgiveindependenceanddominationresultsforsix chess-likepiecesontriangularboardswithtriangularspacesandtriangularboards PrefaceII ix withhexagonalspaces.Thequestionofindependenceanddominationforthesesame boardsonthesurfaceofatetrahedronisintroduced,andsomeinitialresultsaregiven. AgraphhasanefficientdominatingsetifthereexistsasubsetofverticesDsuch thateveryvertexinthegraphisdominatedbyexactlyonevertexinD.LylePaskowitz andhiscoauthorsinvestigateefficientdominationonthestackedversionsofeachof the eleven Archimedean Lattices, and determine the existence or non-existence of efficientdominatingsetsoneachlatticethroughintegerprogramming.Theproofsof existenceareconstructive,andtheproofsofnon-existencearegeneratedbyinteger programs. They find efficient dominating sets on seven of the stacked lattices and provethatnosuchsetsexistontheotherfourstackedlattices. Let G be a graph with vertex setV (G) and edge setE(G). A (p; q)-graph G= (V;E)issaidtobeAL(k)-traversalifthereexistasequenceofverticesv ,v ,...,v 1 2 p suchthatforeachi=1,2,...,p–1,thedistanceforv andv isequaltok.Wecalla i i+1 graphGak-stepsHamiltoniangraphifithasaAL(k)-traversalinGandthedistance betweenv andv isk.AgraphGissaidtobehereditaryk-stepshyperhamiltonian p 1 ifitisk-stepsHamiltonianandforanyvinG,thevertex-deletedsubgraphG\{v} isalsok-stepsHamiltonian.Inthispaper,Hsin-haoSuandhiscoauthorsinvestigate subdivisiongraphsofawheelgraphandC ×K toseewhichare2-stepsHamiltonian 4 2 andhereditarynon2-stepsHamiltonian. LetGbeagraphwithaveragedegreegreaterthank–2.Erdo˝sandSósconjectured that G contains every tree on k vertices as a subgraph. The circumference of the graphG,c(G),isthenumberofedgesonalongestcycle.GilbertandTinerproved thatifc(G)isatmostk,thenGcontainseverytreeonkvertices.HereA.M.Heissan andGaryTinerimprovethisresultandshowthatthe Erdo˝s-Sósconjectureholdsfor graphswhosecircumferenceisatmostk+1. YoshimiEgawaandKenjiKimuraconsiderarelationshipbetweenaregulargraph and a regular factor of its vertex-deleted subgraph. Katerinis proved that if r is an even integer and k is an integer with 1 ≤ k ≤ r/2, and G is an r-regular, r-edge- connectedgraphofoddorder,thenG\{x}hasak-factorforeachx∈V (G).When theresult“foreachx ∈V (G)”ofKaterinisisreplaced“forsomex ∈V (G),”they considerwhatconditioncanhold.Onemainresultis:Letr andk beevenintegers suchthat4≤k≤r/2,and(cid:4)beaminimumintegersuchthat(cid:4)≥r/(r−2k+4),and Gbeanr-regular,2(cid:4)-edge-connectedgraphofoddorder.Then,thereissomex∈V (G) such that G \{x} has a k-factor. Moreover, if r ≥ 4k − 8, then we can replace 2(cid:4)-edge-connectedwith2-edge-connected. In his paper, LeRoy B. Beasley gives several definitions of connectedness and extendibilityofpathsandcyclesindirectedgraphs.Hedefinessetsofdigraphsby varioustypesofconnectednessorextendibilityandgivessomecontainmentsaswell asexamplestoshowpropercontainment. Extraconnectivity generalizes the concept of connectivity of a graph but it is moredifficulttocompute.Inhispaper,EddieChengandhiscoauthorscomputethe g-extraconnectivityofthearrangementgraphforsmallg(g ≤6)withthehelpofa computerprogram.Inaddition,theyprovideanasymptoticresultforgeneralg.
The list of books you might like
