Loading...
|
Please use this identifier to cite or link to this item:
https://nccur.lib.nccu.edu.tw/handle/140.119/94846
|
| Title: | 均勻C超圖的最大邊數 |
| Authors: | 劉逸彰 |
| Contributors: | 張宜武
劉逸彰 |
| Keywords: | 均勻C超圖
Mixed C-hypergraph |
| Date: | 2009 |
| Issue Date: | 2016-05-09 11:58:18 (UTC+8) |
| Abstract: | 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。
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.
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 |
| Reference: | [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. |
| Description: | 碩士
國立政治大學
應用數學系
94751005 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0094751005 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
|
Files in This Item:
| File |
Size | Format | |
|---|
| index.html | 0Kb | HTML2 | 197 | View/Open |
|
All items in 政大典藏 are protected by copyright, with all rights reserved.
|
