| 具有固定匹配数的极值k-部k-一致超图的结构 |
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| 引用本文： | 董晓光,李国全. 具有固定匹配数的极值k-部k-一致超图的结构[J]. 天津师范大学学报(自然科学版), 2013, 33(3): 4-8 |
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| 作者姓名： | 董晓光 李国全 |
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| 作者单位： | 天津师范大学数学科学学院,天津,300387 |
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| 摘 要： | 设V1,V2,…,Vk为k个有限集,i∈{1,2,…,k},ni△=|Vi|,n△=min{n1,n2,…,nk}.H为一个以V1,V2,…,Vk为顶点类的k-部k-一致超图,v(H)表示H的匹配数,|H|表示H的边数.设t为一个给定的整数.首先证明:如果v(H)≤t,则|H|≤tn1n2…nk/n.当v(H)=t,|H|=tn1n2…nk/n时,确定了H的结构.
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| 关 键 词： | 一致超图 匹配数 点覆盖 |
Construction of k-partite k-uniform hypergraphs with fixed matching number which have maximum number of edges |
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| DONG Xiaoguang , LI Guoquan. Construction of k-partite k-uniform hypergraphs with fixed matching number which have maximum number of edges[J]. Journal of Tianjin Normal University(Natural Science Edition), 2013, 33(3): 4-8 |
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| Authors: | DONG Xiaoguang LI Guoquan |
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| Affiliation: | (College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China) |
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| Abstract: | Let V 1,V 2,…,V k be k finite sets.For i∈[k],n i △=｜V i ｜,n△=min{n 1,n 2,…,n k }.H is a k-partite k-uniform hypergraph with vertex sets V 1,V 2,…,V k.The matching number and the edges number of H is denoted by v（H）and ｜H｜ respectively.Let t be a given integer.This study first shows that if v（H）≤t then ｜H｜≤t n 1 n 2 … n k/n,and aims at determining the construction of H which obey the restrictions v（H）= t and ｜H｜ = t n 1 n 2 … n k/n. |
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| Keywords: | uniform hypergraphs matching number vertex cover |
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