简介:AgraphGiscalledchromatic-choosableifitschoicenumberisequaltoitschromaticnumber,namelych(G)=χ(G).Ohba’sconjecturestatesthateverygraphGwith2χ(G)+1orfewerverticesischromaticchoosable.ItisclearthatOhba’sconjectureistrueifandonlyifitistrueforcompletemultipartitegraphs.Recently,Kostochka,StiebitzandWoodallshowedthatOhba’sconjectureholdsforcompletemultipartitegraphswithpartitesizeatmostfive.Butthecompletemultipartitegraphswithnorestrictionontheirpartitesize,forwhichOhba’sconjecturehasbeenverifiedarenothingmorethanthegraphsKt+3,2*(k-t-1),1*tbyEnotomoetal.,andKt+2,3,2*(k-t-2),1*tfort≤4byShenetal..Inthispaper,usingtheconceptoff-choosable(orL0-size-choosable)ofgraphs,weshowthatOhba’sconjectureisalsotrueforthegraphsKt+2,3,2*(k-t-2),1*twhent≥5.Thus,Ohba’sconjectureistrueforgraphsKt+2,3,2*(k-t-2),1*tforallintegerst≥1.
简介:K1,k┐FACTORIZATIONOFBIPARTITEGRAPHSDUBEILIANGAbstract.Inthispaper,anecessaryconditionforabipartitegraphλKm,ntobeK1,k-factoriz...
简介:SupposethatCisthecomplexplaneandkisanon-negativeinteger.DefinefunctionsNk-(x)=|x|kifkisevenandNk(x)=x|x|k-1ifkisodd.SomeapproximationpropertiesofNk-(x)’sisdiscussedandanewexampleofaTchebycheffsystemisgivenout.
简介:Inthispaper,asurfacepotentialbasedthresholdvoltagemodeloffully-depleted(FD)recessed-source/drain(Re-S/D)silicon-on-insulator(SOI)metal-oxidesemiconductorfield-effecttransistor(MOSFET)ispresentedwhileconsideringtheeffectsofhigh-kgate-dielectricmaterialinducedfringing-field.Thetwo-dimensional(2D)Poisson’sequationissolvedinachannelregioninordertoobtainthesurfacepotentialundertheassumptionoftheparabolicpotentialprofileinthetransversedirectionofthechannelwithappropriateboundaryconditions.Theaccuracyofthemodelisverifiedbycomparingthemodel’sresultswiththe2DsimulationresultsfromATLASoverawiderangeofchannellengthsandotherparameters,includingthedielectricconstantofgate-dielectricmaterial.
简介:让G一张连接k的图,和T是V(G)的一个子集。如果G-T没被连接,那么,T被说是G的一个切割集合。G的k-cut-setT是有|T的G的一个切割集合|=k。让T是连接k的图G的k-cut-set。如果G-T能被划分成subgraphsG1和G2以便|G1|2,|G2|2,然后,我们把T称为G的重要k-cut-set。假定G是一(k-1)-connected图没有重要(k-1)-cut-set。然后,我们把G称为伪连接k的图。在这份报纸,我们为任何整数k证明那5,如果没有K4,,G是一张连接k的图,那么,G的每个顶点是有其收缩产出伪的一个边的事件连接k的图,因此有至少\(\frac{{|V(G)|}}{2}\)G的边以便他们的每个成员的收缩导致伪连接k的图。
简介:让一,b,k,r是有1一b和r的nonnegative整数2。让G是有$n的顺序n的一张图>\tfrac{{(+b)(r(+b)-2)+ak}}{一}$。在这份报纸,我们首先为部分的所有显示出描述(一,b,k)批评的图。然后使用结果,我们证明G都是部分的(一,b,k)批评如果$\delta(G)\geqslant\tfrac{{(r-1)b^2}}{一}+k$并且$|N_G(x_1)\cupN_G(x_2)\cup\cdots\cupN_G(x_r)|\geqslant\tfrac{{bn+ak}}{{+b}}$为任何独立子集{x1,x2,,xr}在G。而且,这被显示出条件$|N_G(x_1)上的更低的界限\cupN_G(x_2)\cup\cdots\cupN_G(x_r)|\geqslant\tfrac{{bn+ak}}{{+b}}$是在某感觉可能的最好,并且它是Lus的延期以前的结果。