本文藉構造bipartite graph 的形式討論超圖與對偶超圖的transversal number，進而探討最小著色數的上界，以及證明出此兩圖的最小著色數可差異很大，也可用此方法構造出想要的最小著色數之差異。最後探討在某些情形下，超圖與其對偶超圖的同構性，再則整理出其必要條件。 / H=(X,D) is called a hypergraph, where X is the vertex set and D is a family of subsets of X, denoted as D-edges, and we assume that every D-edges have at least two elements. A strict t-coloring is a onto mapping from X to {1,2,....,t} such that each D contained in D-edge set has two vertices having distinct values. The maximum(minimum) number of colors over all strict k-coloring is called the upper(lower) chromatic number and is denoted as .

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19118号 / 情博第564号 / 新制||情||99(附属図書館) / 32069 / 京都大学大学院情報学研究科社会情報学専攻 / (主査)教授 矢守 克也, 教授 多々納 裕一, 教授 中北 英一 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM