Search results
Results From The WOW.Com Content Network
The Robertson–Seymour theorem states that finite undirected graphs and graph minors form a well-quasi-ordering. The graph minor relationship does not contain any infinite descending chain, because each contraction or deletion reduces the number of edges and vertices of the graph (a non-negative integer). [8]
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.
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. Let H be a fixed graph. Intuitively, if G is a huge H-free graph, then there ought to be a "good reason" for this.
In mathematics, a simple subcubic graph (SSCG) is a finite simple graph in which each vertex has a degree of at most three. Suppose we have a sequence of simple subcubic graphs G 1 , G 2 , ... such that each graph G i has at most i + k vertices (for some integer k ) and for no i < j is G i homeomorphically embeddable into (i.e. is a graph minor ...
Neil Robertson and Paul D. Seymour: Wagner's conjecture: graph theory: Now generally known as the graph minor theorem. 1983: Michel Raynaud: Manin–Mumford conjecture: diophantine geometry: The Tate–Voloch conjecture is a quantitative (diophantine approximation) derived conjecture for p-adic varieties. c.1984: Collective work: Smith ...
By Robertson–Seymour theorem, any set of finite graphs contains only a finite number of minor-minimal elements. In particular, the set of "yes" instances has a finite number of minor-minimal elements. Given an input graph G, the following "algorithm" solves the above problem: For every minor-minimal element H: If H is a minor of G then return ...
Retrieved from "https://en.wikipedia.org/w/index.php?title=Graph_minors_theorem&oldid=1102375387"
Since every minor of a planar graph is itself planar, this gives a planar cover of the minor G. Because the graphs with planar covers are closed under the operation of taking minors, it follows from the Robertson–Seymour theorem that they may be characterized by a finite set of forbidden minors. [7] A graph is a forbidden minor for this ...