The Excluded Minor Structure Theorem with Planarly Embedded Wall
نویسنده
چکیده
A graph is “nearly embedded” in a surface if it consists of graph G0 that is embedded in the surface, together with a bounded number of vortices having no large transactions. It is shown that every large wall (or grid minor) in a nearly embedded graph, many rows of which intersect the embedded subgraph G0 of the near-embedding, contains a large subwall that is planarly embedded within G0. This result provides some hidden details needed for a strong version of the Robertson and Seymour’s excluded minor theorem as presented in [1].
منابع مشابه
Graph minors and graphs on surfaces
Graph minors and the theory of graphs embedded in surfaces are fundamentally interconnected. Robertson and Seymour used graph minors to prove a generalization of the Kuratowski Theorem to arbitrary surfaces [37], while they also need surface embeddings in their Excluded Minor Theorem [45]. Various recent results related to graph minors and graphs on surfaces are presented.
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