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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.
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)
Download as PDF; Printable version; ... move to sidebar hide. From Wikipedia, the free encyclopedia. Redirect page. ... Robertson–Seymour theorem; Retrieved from ...
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]
Robertson–Seymour theorem; Petersen graph; Planar graph. Dual polyhedron; Outerplanar graph; Random graph; Regular graph; Scale-free network; Snark (graph theory) Sparse graph. Sparse graph code; Split graph; String graph; Strongly regular graph; Threshold graph; Total graph; Tree (graph theory). Trellis (graph) Turán graph; Ultrahomogeneous ...
Robertson's example of a non-YΔY-reducible apex graph. A connected graph is YΔY-reducible if it can be reduced to a single vertex by a sequence of steps, each of which is a Δ-Y or Y-Δ transform , the removal of a self-loop or multiple adjacency, the removal of a vertex with one neighbor, and the replacement of a vertex of degree two and its ...
Therefore, the family of pseudoforests is closed under minors, and the Robertson–Seymour theorem implies that pseudoforests can be characterized in terms of a finite set of forbidden minors, analogously to Wagner's theorem characterizing the planar graphs as the graphs having neither the complete graph K 5 nor the complete bipartite graph K 3 ...