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The Robertson–Seymour theorem is named after mathematicians Neil Robertson and Paul D. Seymour, who proved it in a series of twenty papers spanning over 500 pages from 1983 to 2004. [3] Before its proof, the statement of the theorem was known as Wagner's conjecture after the German mathematician Klaus Wagner , although Wagner said he never ...
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.
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]
As the Robertson–Seymour theorem shows, many important families of graphs can be characterized by a finite set of forbidden minors: for instance, according to Wagner's theorem, the planar graphs are exactly the graphs that have neither the complete graph K 5 nor the complete bipartite graph K 3,3 as minors.
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 ...
The Robertson–Seymour theorem proves that, for the particular case of graph minors, a family that is closed under minors always has a finite obstruction set. List of forbidden characterizations for graphs and hypergraphs
The non-constructive part here is the Robertson–Seymour theorem. Although it guarantees that there is a finite number of minor-minimal elements it does not tell us what these elements are. Therefore, we cannot really execute the "algorithm" mentioned above. But, we do know that an algorithm exists and that its runtime is polynomial.
2004 Robertson–Seymour theorem. The proof takes about 500 pages spread over about 20 papers. 2005 Kepler conjecture. Hales's proof of this involves several hundred pages of published arguments, together with several gigabytes of computer calculations.