Ad
related to: robertson seymour theorem equation example questionsstudy.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
Some examples of finite obstruction sets were already known for specific classes of graphs before the Robertson–Seymour theorem was proved. For example, the obstruction for the set of all forests is the loop graph (or, if one restricts to simple graphs, the cycle with three vertices). This means that a graph is a forest if and only if none of ...
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.
This case of the theorem is still provable by Π 1 1-CA 0, but by adding a "gap condition" [3] to the definition of the order on trees above, he found a natural variation of the theorem unprovable in this system. [4] [5] Much later, the Robertson–Seymour theorem would give another theorem unprovable by Π 1 1-CA 0.
Robbins theorem (graph theory) Robertson–Seymour theorem (graph theory) Robin's theorem (number theory) Robinson's joint consistency theorem (mathematical logic) Rokhlin's theorem (geometric topology) Rolle's theorem ; Rosser's theorem (number theory) Rouché's theorem (complex analysis) Rouché–Capelli theorem (Linear algebra)
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 proof involves using Courcelle's theorem to build an automaton that can test the property, and then examining the automaton to determine whether there is any graph it can accept. As a partial converse, [34] Seese (1991) proved that, whenever a family of graphs has a decidable MSO 2 satisfiability problem, the family must have bounded treewidth.
Therefore, by the Robertson–Seymour theorem, the linklessly embeddable graphs have a forbidden graph characterization as the graphs that do not contain any of a finite set of minors. [ 3 ] The set of forbidden minors for the linklessly embeddable graphs was identified by Sachs (1983) : the seven graphs of the Petersen family are all minor ...
exponential diophantine equations: ⇐Pillai's conjecture⇐abc conjecture Mihăilescu's theorem 2002: Maria Chudnovsky, Neil Robertson, Paul D. Seymour, and Robin Thomas: strong perfect graph conjecture: perfect graphs: Chudnovsky–Robertson–Seymour–Thomas theorem 2002: Grigori Perelman: Poincaré conjecture, 1904: 3-manifolds: 2003 ...