| dc.contributor.advisor | 張宜武 | zh_TW |
| dc.contributor.author (Authors) | 劉逸彰 | zh_TW |
| dc.creator (作者) | 劉逸彰 | zh_TW |
| dc.date (日期) | 2009 | en_US |
| dc.date.accessioned | 9-May-2016 11:58:18 (UTC+8) | - |
| dc.date.available | 9-May-2016 11:58:18 (UTC+8) | - |
| dc.date.issued (上傳時間) | 9-May-2016 11:58:18 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0094751005 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/94846 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 94751005 | zh_TW |
| dc.description.abstract (摘要) | 超級混合圖是一個 H = (X,C,D) 的表示法，其中X是代表點集合，而C和D是X的部分子集合，稱為邊。一個嚴格k種顏色可著色法指的是由X的點集對應到{1,2,…,k}的一種關係，其中C代表每一個C邊至少有兩個點同色，而D代表每一個D邊至少有兩個點不同色。C和D都有可能是空集合。假如超過(少於)k並沒有可著色的方法數，則k稱為最大著色數(最小著色數)。而H的每個邊都恰好有r個點則稱為r均勻超級混合圖。 對於r均勻C超級混合圖，如果限定了最大著色數大於等於k的話，則將會改變最大著色數的邊數。如果要找出滿足此條件的最大著色數的最大的邊數，我們主要區分成三種不同的情形來討論，分別是r比k大、r比k小和r = k。 | zh_TW |
| dc.description.abstract (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 k-coloring is a onto mapping from X to {1,2, . . . , k} such that each C ∈ C contains two vertices have a common value and each D ∈ D has two vertices have distinct values. Each of C,D may be empty. The maximum(minimum) number of colors over all strict k-colorings is called the upper(lower) chromatic number of H and is denoted by χ^¯(H)(χ(H)). If a hypergraph H has no multiple edges and all its edges are of size r, then H is called an r-uniform hypergraph. We want to find the maximum number of edges for r-uniform C-hypergraph of order n with the condition χ^¯(H) ≥ k, where k is fixed. We will solve this problem according to three different cases, r < k, r = k and r > k. | en_US |
| dc.description.abstract (摘要) | Abstract ............................i Introduction...........................1 2 Basic concepts on mixed hypergraph coloring...........................3 3 Maximum number of edges of r-uniform C-hypergraphs with n vertices...........................5 4 The minimum number of edges of 2-uniform C-hypergraphs with n vertices...........................21 5 References..................................24 | - |
| dc.description.tableofcontents | Abstract ............................i Introduction...........................1 2 Basic concepts on mixed hypergraph coloring...........................3 3 Maximum number of edges of r-uniform C-hypergraphs with n vertices...........................5 4 The minimum number of edges of 2-uniform C-hypergraphs with n vertices...........................21 5 References..................................24 | zh_TW |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0094751005 | en_US |
| dc.subject (關鍵詞) | 均勻C超圖 | zh_TW |
| dc.subject (關鍵詞) | Mixed C-hypergraph | en_US |
| dc.title (題名) | 均勻C超圖的最大邊數 | zh_TW |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1]M. Gionfriddo, L.Milazzo, and V. Voloshin, On the upper chromatic index of a multigraph, Computer Science J. Moldova 10(2002), 81-91. [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]V. Voloshin, On the upper chromatic number of a hypergraph, Australasian J. Comb. 11(1995), 25-45. [4]V. Voloshin, (2002), Coloring Mixed Hypergraphs: Theory, Algorithms and Applications, American Mathematical Society. | zh_TW |
