(m,n)-樹的判定和計(jì)數(shù).pdf

1、華南師范大學(xué)碩士學(xué)位論文(mn)樹的判定和計(jì)數(shù)姓名：鄧志云申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：運(yùn)籌學(xué)與控制論指導(dǎo)教師：柳柏濂20031001AbstractTreeiSabasicconceptinGraphTheory，anditwasfirst]Yextendedinhigherspacein[2]byBeinekeandPippertLater，itwasdevelopedfurtherinn—dimensionalcomplexesin[1

2、]byDewdney，andtheconceptof(m，n)一treewasobtainedatthesametimeFurthermoreSimilartothetree—characterizationofGraphTheory，thefollowingresultaboutthe(m，n)一treecharacterizationwasgiven：IfKisa(m，n)一tree，thenKsatisfiesthefollowi

3、ngconditions：(1)KiS(m，n)一connected：(2)Kcontainsno(m，n)一circuits：(3)盤。(K)=Bmn(k，K)，where女=12，一，Ⅳ；君(女，足)口o(K)一m—I以一卅㈤一口o(K)一“～1H一，竹時(shí)卜d口。(K)denotesthenumberof≈一dimensionalSimplexesinKInthepaper，onthebasisof[1]and[5]，bycombi

4、ningtheabovethreebasicfeatures，somenewnecessaryandsuffiCientconditionsof(111，n)一treearefirstlygivenAtthelast，bythedefinitionof(m，n)一treeinGraphTheoryandUSingthecombinatorialmethod，thefollowingcountingformulaoflabeled(m，n