Maximum Gap of Mixed Hypergraph
碩士 === 國立政治大學 === 應用數學研究所 === 94 === A mixed hypergraph is a triple H = (X; C;D), where X is the vertex set, and each of C;D is a list of subsets of X. A strict t-coloring is a onto mapping from X to {1, 2,…,t} such that each c belongs to C contains two vertices have a common value and each d belong...
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ndltd-TW-094NCCU55070072015-10-13T10:49:50Z http://ndltd.ncl.edu.tw/handle/86830190408496554950 Maximum Gap of Mixed Hypergraph Kuo, Wei-Ting 郭威廷 碩士 國立政治大學 應用數學研究所 94 A mixed hypergraph is a triple H = (X; C;D), where X is the vertex set, and each of C;D is a list of subsets of X. A strict t-coloring is a onto mapping from X to {1, 2,…,t} such that each c belongs to C contains two vertices have a common value and each d belongs to D has two vertices have distinct values. If H has a strict t-coloring, then t belongs to S(H), such S(H) is called the feasible set of H, and k is a gap if there are a value larger than k and a value less than k in the feasible set but k is not. We find the minimum and maximum gap of a mixed hypergraph with more than 5 vertices. Then we consider two special cases of the gap of mixed hypergraphs. First, if the mixed hypergraphs is spanned by a complete bipartite graph, then the gap is decided by the size of bipartition. Second, the (l,m)-uniform mixed hypergraphs has gaps if l > m/2 >2, and we prove that the minimum number of vertices of a (l,m)-uniform mixed hypergraph which has gaps is (m/2)( l -1) + m. 張宜武 學位論文 ; thesis 15 en_US |
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碩士 === 國立政治大學 === 應用數學研究所 === 94 === A mixed hypergraph is a triple H = (X; C;D), where X is the vertex set, and each of C;D is a list of subsets of X. A strict t-coloring is a onto mapping from X to {1, 2,…,t} such that each c belongs to C contains two vertices have a common value and each d belongs to D has two vertices have distinct values. If H has a strict t-coloring, then t belongs to S(H), such S(H) is called the feasible set of H, and k is a gap if there are a value larger than k and a value less than k in the feasible set but k is not.
We find the minimum and maximum gap of a mixed hypergraph with more than 5 vertices. Then we consider two special cases of the gap of mixed hypergraphs. First, if the mixed hypergraphs is spanned by a complete bipartite graph, then the gap is decided by the size of bipartition. Second, the (l,m)-uniform mixed hypergraphs has gaps if l > m/2 >2, and we prove that the minimum number of vertices of a (l,m)-uniform mixed hypergraph which has gaps is (m/2)( l -1) + m.
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張宜武 |
author_facet |
張宜武 Kuo, Wei-Ting 郭威廷 |
author |
Kuo, Wei-Ting 郭威廷 |
spellingShingle |
Kuo, Wei-Ting 郭威廷 Maximum Gap of Mixed Hypergraph |
author_sort |
Kuo, Wei-Ting |
title |
Maximum Gap of Mixed Hypergraph |
title_short |
Maximum Gap of Mixed Hypergraph |
title_full |
Maximum Gap of Mixed Hypergraph |
title_fullStr |
Maximum Gap of Mixed Hypergraph |
title_full_unstemmed |
Maximum Gap of Mixed Hypergraph |
title_sort |
maximum gap of mixed hypergraph |
url |
http://ndltd.ncl.edu.tw/handle/86830190408496554950 |
work_keys_str_mv |
AT kuoweiting maximumgapofmixedhypergraph AT guōwēitíng maximumgapofmixedhypergraph |
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