Graph minors. XVI. excluding a non-planar graph

Authors:
Neil Robertson;P. D. Seymour
Affiliations:
Ohio State University, Columbus, OH;Telcordia Technologies, 445 South St., Morristown, NJ and Princeton University, Princeton, NJ
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

Citing 8
Cited 79

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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.