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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/5874

    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:[數學學系暨研究所] 研究報告

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