Graph minors. XVI. Excluding a non-planar graph

Neil Robertson; P. D. Seymour

doi:10.1016/S0095-8956(03)00042-X

Graph minors. XVI. Excluding a non-planar graph

Neil Robertson, P. D. Seymour

Mathematics

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251 Scopus citations

Abstract

This paper contains the cornerstone theorem of the series. We study the structure of graphs with no minor isomorphic to a fixed graph L, when L is non-planar. (The case when L is planar was studied in an earlier paper.) We find that every graph with no minor isomorphic to L may be constructed by piecing together in a tree-structure graphs each of which "almost" embeds in some surface in which L cannot be embedded.

Original language	English (US)
Pages (from-to)	43-76
Number of pages	34
Journal	Journal of Combinatorial Theory. Series B
Volume	89
Issue number	1
DOIs	https://doi.org/10.1016/S0095-8956(03)00042-X
State	Published - Sep 2003

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/S0095-8956(03)00042-X

Cite this

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Graph minors. XVI. Excluding a non-planar graph

Abstract

All Science Journal Classification (ASJC) codes

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