Excluding Minors in Nonplanar Graphs of Girth at Least Five
Excluding Minors in Nonplanar Graphs of Girth at Least Five
复制标题
在至少五周长的非平面图中排除未成年人
DOI：
10.1017/s0963548300004417
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Jan Mcdonald Thomson
中科院分区：
文献类型：
--
作者：
R. Thomas;Jan Mcdonald Thomson
一个图G是拟4连通的，如果它是简单的，3-连通的，至少有5个顶点，并且对于V(G)的每个划分(A，B，C)，或者是[MID]C[MID][GES]4，或者G有一条边，它的一端在A，另一端在B，或者A，B中的一个至多有一个顶点。证明了任何最小度至少为3且不存在长度小于5的圈的拟4连通非平面图有一个次同构于P-Petersen图，P-−10去掉了一条边.我们证明了Tutte四流猜想的弱化：每一个没有次同构于P−10的2-边连通图都有一个非零4-流。这推广了Kilakos和Shepherd的一个结果，他们对3-正则图证明了同样的结果。
A graph G is quasi 4-connected if it is simple, 3-connected, has at least five vertices, and for every partition (A, B, C) of V(G) either [mid ]C[mid ] [ges ] 4, or G has an edge with one end in A and the other end in B, or one of A,B has at most one vertex. We show that any quasi 4-connected nonplanar graph with minimum degree at least three and no cycle of length less than five has a minor isomorphic to P−10, the Petersen graph with one edge deleted. We deduce the following weakening of Tutte's Four Flow Conjecture: every 2-edge-connected graph with no minor isomorphic to P−10 has a nowhere-zero 4-flow. This extends a result of Kilakos and Shepherd who proved the same for 3-regular graphs.