In graph theory, the Robertson–Seymour theorem (also called the graph minors theorem) states that the undirected graphs, partially ordered by the graph...

published over a span of many years, in which they proved the Robertson–Seymour theorem (formerly called Wagner's Conjecture). This states that families...

topological embeddings. The theorem is stated in the seventeenth of a series of 23 papers by Neil Robertson and Paul Seymour. Its proof is very long and...

04994. doi:10.1112/plms.12504. S2CID 259380697. Robertson–Seymour theorem Strong perfect graph theorem Seymour, Paul. "Online Papers". Retrieved 26 April 2013...

theory of graph minors and can be seen as a forerunner of the Robertson–Seymour theorem. A planar embedding of a given graph is a drawing of the graph...

2004, the result was generalized from trees to graphs as the Robertson–Seymour theorem, a result that has also proved important in reverse mathematics...

published it in 1970. In the course of their proof, Seymour and Robertson also prove the graph structure theorem in which they determine, for any fixed graph...

possible to find in polynomial time whether H is a minor of G. By Robertson–Seymour theorem, any set of finite graphs contains only a finite number of minor-minimal...

forbidden minors; therefore, these two theorems are equivalent. An extension is the Robertson–Seymour theorem. Kelmans–Seymour conjecture, that 5-connected nonplanar...

on graph minors leading to the Robertson–Seymour theorem and the graph structure theorem, Neil Robertson and Paul Seymour proved that a family F of finite...

Tree decomposition. Robertson & Seymour 1991, Theorem 5.1, p. 168. Seymour & Thomas (1994). Robertson & Seymour (1991), Theorem 4.1, p. 164. Bodlaender...

family must have bounded treewidth. The proof is based on a theorem of Robertson and Seymour that the families of graphs with unbounded treewidth have arbitrarily...

"forbidden minors". This is now the Robertson–Seymour theorem, proved in a long series of papers. In the language of this theorem, K5 and K3,3 are the forbidden...

homeomorphically embeddable into (i.e. is a graph minor of) Gj. The Robertson–Seymour theorem proves that subcubic graphs (simple or not) are well-founded by...

called a Kuratowski subgraph. A generalization, following from the Robertson–Seymour theorem, asserts that for each integer g, there is a finite obstruction...

substructure is, this obstruction set could be infinite. The Robertson–Seymour theorem proves that, for the particular case of graph minors, a family...

forbidden minors analogously to Wagner's theorem characterizing the planar graphs. Neil Robertson and Paul Seymour finally published a proof of Wagner's...

Neil Robertson, Paul Seymour, and Robin Thomas was announced in 2002 and published by them in 2006. The proof of the strong perfect graph theorem won for...

graph formed from G by contracting and removing edges. As the Robertson–Seymour theorem shows, many important families of graphs can be characterized...

Tutte's spring theorem applies in this case. Toroidal graphs also have book embeddings with at most 7 pages. By the Robertson–Seymour theorem, there exists...

MR 1427555, S2CID 14962541 Robertson, Neil; Sanders, Daniel P.; Seymour, Paul; Thomas, Robin (1997), "The Four-Colour Theorem", J. Combin. Theory Ser. B...

concrete algorithm is known for solving them. For example, the Robertson–Seymour theorem guarantees that there is a finite list of forbidden minors that...

endpoint along the path of the contracted edge. Therefore, by the Robertson–Seymour theorem, the linklessly embeddable graphs have a forbidden graph characterization...

Vigoda, for approximating the permanent. Neil Robertson and Paul Seymour, for the Robertson–Seymour theorem showing that graph minors form a well-quasi-ordering...

Ramsey's theorem (graph theory, combinatorics) Ringel–Youngs theorem (graph theory) Robbins' theorem (graph theory) Robertson–Seymour theorem (graph theory)...

2007) Robertson–Seymour theorem (Neil Robertson, Paul Seymour, 2004) Strong perfect graph conjecture (Maria Chudnovsky, Neil Robertson, Paul Seymour and...

improper Interval graph, proper Line graph Lollipop graph Minor Robertson–Seymour theorem Petersen graph Planar graph Dual polyhedron Outerplanar graph...

minors; then it may be called a minor-hereditary property. The Robertson–Seymour theorem implies that a minor-hereditary property may be characterized...

minor they do not allow deleting edges. For graph minors, the Robertson–Seymour theorem states that any graph property closed under minors has finitely...

and therefore have a forbidden minor characterization (by the Robertson–Seymour theorem). The graphs of the Petersen family constitute some (but not all)...