简介：ItisshownthatifGisahamiltonianbipartitegraphon2nverticesandδ(G)>2n/5+2,wheren≥60,thenGisbipancyclic.

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简介：H.WangconsideredtheminimumdegreesconditionthatGhaslargevertexdisjointcyclesinbipartitegraphs.Motivatedbythis,weconsiderthesmallvertex-disjointcyclesinbipartitegraphsinthispaper.Weprovethefollowingresult:Letm≥3,n≥2andk≥1bethreeintegers.LetG=(V1,V2;E)beabipartitegraphwith|V1|=|V2|=n≥2k+1.Iftheminimumdegreeδ(G)≥k+1andx∈V(C)^∑d(x)≥m(n+1)+1foranycycleCofGwithlength2m,thenGcontainskvertex-disjointcyclesoflength4.Moreover,thedegreesconditionissharp.

简介：Inthispapertheauthorsgeneralizetheclassicrandombipartitegraphmodel,anddefineamodeloftherandombipartitemultigraphsasfollows:letm=m(n)beapositiveinteger-valuedfunctiononnandζ(n,m;{pk})theprobabilityspaceconsistingofallthelabeledbipartitemultigraphswithtwovertexsetsA={a_1,a_2,...,a_n}andB={b_1,b_2,...,b_m},inwhichthenumberst_(ai),b_joftheedgesbetweenanytwoverticesa_i∈Aandb_j∈BareidenticallydistributedindependentrandomvariableswithdistributionP{t_(ai),b_j=k}=pk,k=0,1,2,...,wherepk≥0and∞Σk=0pk=1.TheyobtainthatX_(c,d,A),thenumberofverticesinAwithdegreebetweencanddofG_(n,m)∈ζ(n,m;{pk})hasasymptoticallyPoissondistribution,andanswerthefollowingtwoquestionsaboutthespaceζ(n,m;{pk})with{pk}havinggeometricdistribution,binomialdistributionandPoissondistribution,respectively.Underwhichconditionfor{pk}cantherebeafunctionD(n)suchthatalmosteveryrandommultigraphG_(n,m)∈ζ(n,m;{pk})hasmaximumdegreeD(n)inA?underwhichconditionfor{pk}hasalmosteverymultigraphG(n,m)∈ζ(n,m;{pk})auniquevertexofmaximumdegreeinA?

简介：Givennon-negativeintegersm,n,handkwithm≥h>1andn≥k>1,an(h,k)-bipartitehypertournamentonm+nverticesisatriple(U,V,A),whereUandVaretwosetsofverticeswith|U|=mand|V|=n,andAisasetof(h+k)-tuplesofvertices,calledarcs,withatmosthverticesfromUandatmostkverticesfromV,suchthatforanyh+ksubsetsU_1∪V_1ofU∪V,Acontainsexactlyoneofthe(h+k)!(h+k)-tupleswhoseentriesbelongtoU_1∪V_1.Necessaryandsufficientconditionsforapairofnon-decreasingsequencesofnon-negativeintegerstobethelosingscorelistsorscorelistsofsome(h,k)-bipartitehypertournamentareobtained.

简介：LiuandYangavethedegreeconditionforabalancedbipartitegraphG=(V_1,V_2;E)tohavekvertex-disjointquadrilateralscontaininganygivenkindependentedgese_1,...,e_kofG,respectively.Theyalsoconjecturedthatforanykindependentedgese_1,...,e_kofG,Ghasa2-factorwithkcyclesC_1,C_2,…,C_kwithrespectto{e_1,e_2,...,e_k}suchthatk-1ofthemarequadrilaterals.Inthispaper,weprovethisconjecture.

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简介：象建议，当模特儿的话题，和医药诊断一样的许多机器学习和数据采矿(MLDM)问题能在由两部组成的图上作为计算被建模。然而，很分布式的图平行系统对在这的唯一的特征忘却图和存在的联机图划分算法通常在网络通讯上象重要压力一样引起顶点的过多的复制。这篇文章识别为分布式的MLDM处理划分由两部组成的图的挑战和机会并且建议BiGraph，划分算法的一套由两部组成面向的图。BiGraph力量观察象数据在导出一套最佳的图的顶点的二个子集之间缩放划分导致最小的顶点复制和网络通讯的算法的顶点，区别计算负担和imbalanced的扭曲的分发那样。BiGraph在PowerGraph上被实现了并且被显示有表演增加直到17.75X(从1.16X)为四个典型MLDM算法，由于减少直到80%顶点复制，并且直到96%网络交通。

简介：Ｋ１，ｋ┐ＦＡＣＴＯＲＩＺＡＴＩＯＮＯＦＢＩＰＡＲＴＩＴＥＧＲＡＰＨＳＤＵＢＥＩＬＩＡＮＧＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ，ａｎｅｃｅｓｓａｒｙｃｏｎｄｉｔｉｏｎｆｏｒａｂｉｐａｒｔｉｔｅｇｒａｐｈλＫｍ，ｎｔｏｂｅＫ１，ｋ－ｆａｃｔｏｒｉｚ...

简介：Basedonthebipartiteentangledstaterepresentationandusingthetechniqueofintegrationwithinanorderedproduct(IWOP)ofoperatorsweconstructthecorrespondingoperatorFredholmequationsandthenderivetheirsolutions.Asitsapplicationwededucesomenewbosonicoperatoridentitiesandnewrelationsaboutthetwo-variableHermitepolynomials.

简介：Theeffectsofmeasurementnoiseareinvestigatedinthecontextofbipartiteconsensusofmulti-agentsystems.Inthesystemsetting,discrete-timedouble-integratordynamicsareassumedfortheagent,andmeasurementnoiseispresentfortheagentreceivingthestateinformationfromitsneighbors.Time-varyingstochasticbipartiteconsensusprotocolsaredesignedinordertolessentheharmfuleffectsofthenoise.Consequently,thestatetransitionmatrixoftheclosed-loopsystemisanalyzed,andsufficientandnecessaryconditionsfortheproposedprotocoltobeameansquarebipartiteconsensusprotocolaregivenwiththehelpoflineartransformationandalgebraicgraphtheory.Itisproventhatthesigneddigraphtobestructurallybalancedandhavingaspanningtreearetheweakestcommunicationassumptionsforensuringbipartiteconsensus.Inparticular,theproposedprotocolisameansquarebipartiteaverageconsensusoneifthesigneddigraphisalsoweightbalanced.

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