圖之分割與其著色之探討

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Research Paper > Item 987654321/5874

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Title:	圖之分割與其著色之探討
Other Titles:	The Study of Graph Decomposition and Its Coloring
Authors:	高金美
Contributors:	淡江大學數學學系
Keywords:	圖的分割;組合設計;區組集;迴圈設計graph decomposition;combinatorial design;blocking set;cycle design.
Date:	2006
Issue Date:	2009-03-16 13:04:17 (UTC+8)
Abstract:	圖的分割就是將圖分割成幾個子圖使得各個子圖的邊都相異。如果這些子圖都同構且原圖為一個完全圖，我們稱之為此種子圖的設計。如果這些子圖都是迴圈，我們稱之為迴圈設計。在完全圖之頂點集合中找到一個子集，使得所有的迴圈與其交集都不是空集合，且此子集不能含有任一迴圈的所有頂點，我們稱此子集為區組集。因為我們知道一個三迴圈設計除了只含三個點的完全圖外，其餘均沒有區組集，且一個組合設計之區組集已經被研究多年，在此計畫中我們是希望探討什麼樣的迴圈設計能有區組集，也就是說中什麼樣的迴圈設計之每一個頂點著色後其每一個迴圈中都含有兩個顏色？ A graph can be partitioned into edge disjoint sub-graphs is called a graph decomposition. If these sub-graphs are isomorphic and the original graph is a complete graph, then we call this is a design. If these sub-graphs are cycles, then we call it is a cycle design. If S is a subset of the vertex set of the complete graph, and the intersection of each cycle and S is not empty, and There is no cycle contained in S, then we call S is the blocking set. Since we know that there is no blocking set in a 3-cycle system except there is only three vertices. The research about a blocking set of a combinatorial design is studied so many years. In this project we try to study what kind cycle design may have blocking set, i.e. what kind cycle design can be 2-colorable.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Research Paper

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