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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.
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.
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 Graph minor [3] Linklessly embeddable graphs: The Petersen family ...
A minor of a graph G is any graph H that is isomorphic to a graph that can be obtained from a subgraph of G by contracting some edges. If G does not have a graph H as a minor, then we say that G is H-free.
This states that families of graphs closed under the graph minor operation may be characterized by a finite set of forbidden minors. As part of this work, Robertson and Seymour also proved the graph structure theorem describing the graphs in these families. [6] Additional major results in Robertson's research include the following:
Pages in category "Graph minor theory" The following 33 pages are in this category, out of 33 total. ... Robertson–Seymour theorem; S. Shallow minor; Snark (graph ...
Retrieved from "https://en.wikipedia.org/w/index.php?title=Graph_minors_theorem&oldid=1102375387"
In the following, the notation of Mansouri–Sexl is used. [2] They chose the coefficients a, b, d, e of the following transformation between reference frames: = + = = = where T, X, Y, Z are the Cartesian coordinates measured in a postulated preferred frame (in which the speed of light c is isotropic), and t, x, y, z are the coordinates measured in a frame moving in the +X direction (with the ...