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    題名: Oberwolfach 問題及其推廣的探討
    其他題名: The Study of Oberwolfach Problem and Its Generalization
    作者: 高金美
    貢獻者: 淡江大學數學學系
    日期: 2012-08
    上傳時間: 2015-05-12 15:30:39 (UTC+8)
    摘要: 一個圖中任兩點都相鄰,稱之為完全圖, m 個點的完全圖記為Km 。每點度數均為 2 的n 個點連通圖稱為n-迴圈,記為Cn。一個2-因子是指Km 中的一個含有m 個點的子 圖且每一點的度數都為2。圖的分割是指將圖G 分成數個邊相異的子圖G1, G2, …, Gt, 且 G 的每一邊會落在唯一的一個子圖Gi 上。Oberwolfach problem 是探討一個含有2k+1 個點的完全圖K2k+1 是否能分割成一些邊都相異的2-因子,且每個2-因子中的迴圈均對 應相同呢? Hamilton-Waterloo problem 是Oberwolfach problem 的推廣。 Hamilton-Waterloo problem 是探討一個含有2k+1 個點的完全圖K2k+1 是否能分割成一些 邊都相異的2-因子,且此2-因子中的迴圈均相同,但是其中共含有兩種2-因子呢? 在此計畫中,我們將針對尚未解決的 Oberwolfach problem, Hamilton-Waterloo problem 及其推廣作一些研究,希望能找到完全圖分割成所想要的兩種或三種2-因子的 充分必要條件。
    A graph in which any two distinct vertices are adjacent is called a complete graph, Km. An n-cycle Cn is a connected graph with n vertices and all have degree 2. A 2-factor of Km is a subgraph of Km with m vertices and the degree of each vertex is 2. A decomposition of a graph is a collection of edge-disjoint subgraphs G1, G2, …, Gn of G such that every edge of G belongs to exactly one Gi. The Oberwolfach problem is the existence of the decomposition of K2k+1 into 2-factors such that each 2-factors contains the same cycles. The Hamilton-Waterloo problem is the existence of the decomposition of K2k+1 into two kinds of 2-factors such that each kind 2-factor contains exactly only one kind cycle . In this project, we will find some solutions of Oberwolfach problem, Hamilton-Waterloo problem and their generalization. Hope that we can find the necessary and sufficient conditions of the decomposition of complete graph Km into two kinds or three kinds 2-factors.
    顯示於類別:[數學學系暨研究所] 研究報告

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