【摘要】：給定一無(wú)向圖G=(V,E),一對(duì)多的k可覆蓋的定義:內(nèi)部存在k條點(diǎn)不交的從任意一個(gè)源到任意k個(gè)匯的路覆蓋圖中每一個(gè)點(diǎn).在文獻(xiàn)[1]中,Park等人確立了一個(gè)充要條件,對(duì)任意的連通圖的立方圖都有一個(gè)連接一個(gè)源和三個(gè)匯點(diǎn)的一對(duì)多的3不交路覆蓋.由于一個(gè)圖的k可覆蓋性需要點(diǎn)的連通度比較高,他找到了連通圖的立方圖存在一對(duì)多的3覆蓋的充要條件,于是他考慮降低一下點(diǎn)的連通度,如2連通圖的平方圖是否也具有一對(duì)多的3可覆蓋性.在文中,將展示2連通圖的平方圖是一對(duì)多的3可覆蓋的.即2連通圖的平方圖總有一個(gè)3-DPC.
[Abstract]:Given an undirected graph G = (VVX E), the definition of a one-to-many k-covered graph is that there exists every point in the path covering graph with k disjoint points from any source to any k sink. In reference [1], Park et al established a sufficient and necessary condition that a one-to-many 3-disjoint path covering a cubic graph of any connected graph has a one-to-many one to many connected source and three meeting points. Because the k coverage of a graph requires a higher connectivity of a point, he finds a sufficient and necessary condition for a cubic graph of a connected graph to have a one-to-many 3-covering, so he considers reducing the connectivity of a given point. For example, whether the square graph of 2 connected graph also has 3 covering property of one to many. In this paper, we show that the square graph of 2-connected graph is one-to-many 3-covered. That is, the square graph of 2-connected graph always has a 3-DPC.
【學(xué)位授予單位】：新疆大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

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