α-可分解的圈系統(tǒng).pdf

1、河北師范大學(xué)碩士學(xué)位論文α可分解的圈系統(tǒng)姓名：馬秀文申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：田子紅20080320AbstractInthispaperwediscusstheexistenceoftheQresolvablecyclesystemsandframegeneralizedbalancedtournamentdesignsLetA石乙(AD局0)be(directed)completemultigraphoforder“

2、andindexAAcycleoflengthmisasequenceofmdistinctverticesU1，U2，，亂m，denotedby(U1，U2，，um)，anditsedgesetisu，lti1)：i=1，2，，m一1uUl，U仇AdirectedcycleoflengthmisasequenceofmdistinctverticesU1，1／2，，“m。denotedby(Ul，U2，，亂m)。anditsdirec

3、tededgesetis(ut，Ui1)：i=1，2，，m一1)u(札m，札1))Ifthe(directed)edgesofaAK(ADKv)canbedecomposedinto(directed)cyclesoflengthm，thenthese(directed)cyclesalecalleda(directed)m—cyclesystem，anddenotedbymCS(v，A)(mDCS(v，入))AnmCS(v，A)(mD

4、CS(v，A))issaidtobeQ—resolvableifits(directed)cyclescanbepartitionedintoclasses(calledOtresolutionclasses)suchthateachpointofthedesignoccursinpreciselyDcyclesineachclassInthefirstpartofthispaperwederivetheexistenceoftheQ—

5、resolvable4CS(v，A)ando—resolvablem—DCS(v，A)for“2=3，4Iftheblocksofa(4，3)一GDD(X，鄉(xiāng)，召)oftypegucanbearrangedintoa(gu／4)guarraywithproperties：(1)themaindiagonalconsistsofuemptysubarraysofsize(g／4)夕：(2)theblocksineachcolumnform

6、apartial1resolutionclassespartitioningX＼GforsomeG∈9，whiletheblocksineachrowformapartial4resolutionclassespartitioningX＼GforsomeG∈9，thenitiscalledaflamegeneralizedbalancedtournamentdesign，anddenotedbyFGBTD(4，gU)Inthesecon