Excluded minors in cubic graphs
Excluded minors in cubic graphs
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DOI：
10.1016/j.jctb.2019.02.002
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发表时间：
2014-03
期刊：
影响因子：
--
通讯作者：
N. Robertson;P. Seymour;R. Thomas
中科院分区：
文献类型：
--
作者：
N. Robertson;P. Seymour;R. Thomas
设G是一个围长至少为5的三次图，使得对G的顶点集的每个划分X，Y，|X|,|Y| ≥ 7 X和Y之间至少有六条边。我们证明了如果G中没有Petersen图的同胚嵌入，并且G不是一个特殊的20-顶点图，那么·G v对于某个顶点v是平面的;或者· G可以在平面上画有交叉，但只有两个交叉，都在无限区域上。我们还证明了其他几个同类定理。
Let G be a cubic graph, with girth at least five, such that for every partition X, Y of its vertex set with| X|,| Y|≥ 7 there are at least six edges between X and Y. We prove that if there is no homeomorphic embedding of the Petersen graph in G, and G is not one particular 20-vertex graph, then either• G∖ v is planar for some vertex v; or• G can be drawn with crossings in the plane, but with only two crossings, both on the infinite region. We also prove several other theorems of the same kind.