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A similar theorem states that K 4 and K 2,3 are the forbidden minors for the set of outerplanar graphs. Although the Robertson–Seymour theorem extends these results to arbitrary minor-closed graph families, it is not a complete substitute for these results, because it does not provide an explicit description of the obstruction set for any family.
Robertson has won the Fulkerson Prize three times, in 1994 for his work on the Hadwiger conjecture, in 2006 for the Robertson–Seymour theorem, and in 2009 for his proof of the strong perfect graph theorem. [11] He also won the Pólya Prize (SIAM) in 2004, the OSU Distinguished Scholar Award in 1997, and the Waterloo Alumni Achievement Medal ...
Another result relating the four-color theorem to graph minors is the snark theorem announced by Robertson, Sanders, Seymour, and Thomas, a strengthening of the four-color theorem conjectured by W. T. Tutte and stating that any bridgeless 3-regular graph that requires four colors in an edge coloring must have the Petersen graph as a minor. [15]
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 involved. Its proof is very long and involved. Kawarabayashi & Mohar (2007) and Lovász (2006) are surveys accessible to nonspecialists, describing the theorem and its consequences.
In the first of their famous series of papers on graph minors, Neil Robertson and Paul Seymour define a path-decomposition of a graph G to be a sequence of subsets X i of vertices of G, with two properties: For each edge of G, there exists an i such that both endpoints of the edge belong to subset X i, and
Robertson, Seymour & Thomas (1993) proved the conjecture for =, also using the four color theorem; their paper with this proof won the 1994 Fulkerson Prize. It follows from their proof that linklessly embeddable graphs , a three-dimensional analogue of planar graphs, have chromatic number at most five. [ 3 ]
Paul D. Seymour FRS (born 26 July 1950) is a British mathematician known for his work in discrete mathematics, especially graph theory.He (with others) was responsible for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the perfect graph conjecture, the Hadwiger conjecture, claw-free graphs, χ ...
Pages in category "Theorems in statistics" The following 55 pages are in this category, out of 55 total. ... Le Cam's theorem; Lehmann–Scheffé theorem;