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- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing AG 2017
- ISBN
- 978-3-319-66064-6
- Pages
- 85 –97
- DOI
- 10.1007/978-3-319-66065-3_4
- Publisher site
- See Chapter on Publisher Site
Abstract
[The Graph Minor Theorem of Robertson and Seymour associates, to any graph property whatsoever, a finite, characteristic list of graphs. We view this as an impressive generalization of Kuratowski’s theorem, which defines planarity in terms of two forbidden subgraphs, K5 and K3,3. Robertson and Seymour’s result empowers students to devise their own Kuratowski type theorems; we propose several undergraduate research projects with that goal. As an explicit example, we determine the seven forbidden minors for a property we call strongly almost–planar (SAP). A graph is SAP if, for any edge e, both deletion and contraction of e result in a planar graph.]
Published: Jan 6, 2018