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最大,二分,外平面圖之容忍表示法 / The Tolerance Representations of Maximal Bipartite Outerplanar Graphs賴昱儒 Unknown Date (has links)
在這篇論文中,我們針對2-連通的最大外平面圖而且是二分圖的圖形,討論
其容忍表示法,並找到它的所有禁止子圖H1、H2、H3、H4。 / In this thesis, we prove a 2-connected graph G which is maximal outerplanar and bipartite is a tolerance graph if and only if there is no induced subgraphs H1; H2; H3 and H4 of G.
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最大外平面圖的有界容忍表示法 / Bounded Tolerance Representation for Maximal Outerplanar Graphs郭瓊雲 Unknown Date (has links)
本文針對2-連通的最大外平面圖,討論其有界容忍表示法,且找到禁止子圖S3。我們更進一步證明:如果一個2-連通的最大外平面圖恰有兩個點的度為2時,則此圖為區間圖。 / We prove that a 2-connected maximal outerplanar graph G is a bounded tolerance graph if and only if there is no induced subgraph S3 of G and G has no
induced subgraph S3 if and only if G is an interval graph.
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系列平行圖的長方形數與和絃圖數 / The Boxicity and Chordality of a Series-Parallel Graph周佳靜 Unknown Date (has links)
一個圖形G = (V,E),如果可以找到最小k個和弦圖,則此圖形G = (V,E)的和弦圖數是k。
在這篇論文中,我們呈現存在一個系列平行圖的boxicity是3,且和弦圖數是1或2,存在一個平面圖形的和弦圖數是3。 / The chordality of G = (V,E) is dened as the minimum k such that we can write E = E1n...nEk, where each (V,Ei) is a chordal graph.
In this thesis, we present that (1) there are series-parallel graphs with boxicity 3, (2) there are series-parallel graphs with chordality 1 or 2, and (3) there are planar graphs with chordality 3.
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探討平面圖的d維矩形表示法 / A Study on Strict d-box Representations of Planar Graphs劉淑慧 Unknown Date (has links)
本文我們探討平面圖形的嚴格d維矩形表示法。我們證明了四連通三角平面圖有嚴格的二維矩形表示法,而且我們推廣到每一個平面圖都有嚴格的三維矩形表示法。我們的目標是希望能在平面圖矩形表示法的現今地位上,提供新的洞悉,並給未來學習者一個方向。 / We study strict d-box representations of planar graphs. We prove that a 4-connected planar triangulation graph G has a strict 2-box representation. We extend this result to that every planar graph has a strict 3-box representation. Our goal is to provide some fresh insights into the current status of research in the area while suggesting directions for the future.
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