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https://nccur.lib.nccu.edu.tw/handle/140.119/32613
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| Title: | Maximum Gap of Mixed Hypergraph |
| Authors: | 郭威廷
Kuo, Wei-Ting |
| Contributors: | 張宜武
郭威廷
Kuo, Wei-Ting |
| Keywords: | mixed hypergraph
feasible set
gap |
| Date: | 2005 |
| Issue Date: | 2009-09-17 13:50:58 (UTC+8) |
| Abstract: | 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. |
| Reference: | [1] E. Bulgaru and V. Voloshin, Mixed interval hypergraphs, Discrete Applied Math. 77
(1997), 29–41.
[2] T. Jiang, D. Mubayi, Z. Tuza, V. Voloshin, and D. West, The chromatic spectrum of
mixed hypergraphs, Graphs Combin. 18 (2003), 309–318.
[3] D. Kr´al’, J. Kratochv´il, and H. Voss, Mixed hypercacti, Discrete Math. 286 (2004),
99–113.
[4] M. Gionfriddo, L. Milazzo, and V. Voloshin, On the upper chromatic index of a
multigraph, Computer Science J. Moldova 10 (2002), 81–91.
[5] V. Voloshin, On the upper chromatic number of a hypergraph, Australasian J. Comb.
11 (1995), 25–45. |
| Description: | 碩士
國立政治大學
應用數學研究所
92751017
94 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0927510171 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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