Ad
related to: robertson seymour theorem practice teststudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
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.
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 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.
Kuratowski's theorem: K 5 and K 3,3: Graph minor Wagner's theorem: Outerplanar graphs: K 4 and K 2,3: Graph minor Diestel (2000), [1] p. 107: Outer 1-planar graphs: Six forbidden minors Graph minor Auer et al. (2013) [2] Graphs of fixed genus: A finite obstruction set Graph minor Diestel (2000), [1] p. 275: Apex graphs: A finite obstruction set ...
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 ...
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.
As Nešetřil & Thomas (1985) observed, linklessly embeddable graphs are closed under graph minors, from which it follows by the Robertson–Seymour theorem that a forbidden graph characterization exists. The proof of the existence of a finite set of obstruction graphs does not lead to an explicit description of this set of forbidden minors ...
Retrieved from "https://en.wikipedia.org/w/index.php?title=Graph_minors_theorem&oldid=1102375387"