The 2 and 3 representative projective planar embeddings
The 2 and 3 representative projective planar embeddings
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2 和 3 具有代表性的投影平面嵌入
DOI：
10.1016/0095-8956(92)90063-4
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
R. Vitray
中科院分区：
文献类型：
--
作者：
R. Vitray
一个嵌入在曲面上的图是非表示的，如果曲面中的每一条不与嵌入边相交的非平凡闭曲线必须至少包含图的n个顶点。在曲面上的n-代表性的性质在较小的包含下向上封闭，因此，由N.罗伯逊和P. D。Seymour（Graph Minors）八.一个Kuratowski定理一般曲面，提交出版），一个表面上的小极小n-代表嵌入的集合是有限的同构。作为次极小n-代表的性质在Y-Δ运算下是不变的。求出了射影平面上的次极小2和3代表嵌入的集合，并利用这些嵌入生成拓扑极小2和3代表射影嵌入。
A graph embedded on a surface isn-representativeif every nontrivial closed curve in the surface which does not intersect edges of the embedding must contain at leastnvertices of the graph. The property of beingn-representative on a surface is closed upward under minor inclusion; hence, by the results ofN. Robertson and P. D. Seymour (Graph minors. VIII. A Kuratowski theorem for general surfaces, submitted for publication), the set of minor minimaln-representative embeddings on a surface is finite up to isomorphism. The property of being minor minimaln-representative is invariant underY-Δoperations. The set of minor minimal 2 and 3 representative embeddings on the projective plane are found. These embeddings are used to produce the topologically minimal 2 and 3 representative projective embeddings.