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https://ah.lib.nccu.edu.tw/handle/140.119/32613
題名: | Maximum Gap of Mixed Hypergraph | 作者: | 郭威廷 Kuo, Wei-Ting |
貢獻者: | 張宜武 郭威廷 Kuo, Wei-Ting |
關鍵詞: | mixed hypergraph feasible set gap |
日期: | 2005 | 上傳時間: | 17-Sep-2009 | 摘要: | 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.\nWe 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. | 參考文獻: | [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. |
描述: | 碩士 國立政治大學 應用數學研究所 92751017 94 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0927510171 | 資料類型: | thesis |
Appears in Collections: | 學位論文 |
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51017101.pdf | 43.91 kB | Adobe PDF2 | View/Open | |
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