Search results
Results from the WOW.Com Content Network
The vertex-connectivity statement of Menger's theorem is as follows: . Let G be a finite undirected graph and x and y two nonadjacent vertices. Then the size of the minimum vertex cut for x and y (the minimum number of vertices, distinct from x and y, whose removal disconnects x and y) is equal to the maximum number of pairwise internally disjoint paths from x to y.
For arbitrary graph families, and arbitrary sentences, this problem is undecidable. However, satisfiability of MSO 2 sentences is decidable for the graphs of bounded treewidth, and satisfiability of MSO 1 sentences is decidable for graphs of bounded clique-width. The proof involves using Courcelle's theorem to build an automaton that can test ...
For the special case of a square of a planar graph, Wegner conjectured in 1977 that the chromatic number of the square of a planar graph is at most max(Δ + 5, 3Δ / 2 + 1), and it is known that the chromatic number is at most 5Δ / 3 + O(1). [6] [7] More generally, for any graph with degeneracy d and maximum degree Δ, the ...
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
The good news is that the farrier is in the area and can shoe your horse right away. However, in all the excitement your horse is having far too much fun to be caught.
A gay Georgia couple convicted of sickening sexually abuse of their two adopted sons will spend the rest of the lives behind bars.. William and Zachary Zulock, 34 and 36, were each sentenced last ...
December 18, 2024 at 4:57 AM. Danielle Bradley and Ashling Graham say they have been let down by the justice system after their father's killer went on the run from prison once again [BBC]
A 1-regular graph has no cycle, and a connected 2-regular graph has girth equal to its number of vertices, so cages are only of interest for r ≥ 3. The (r,3)-cage is a complete graph K r + 1 on r + 1 vertices, and the (r,4)-cage is a complete bipartite graph K r,r on 2r vertices. Notable cages include: (3,5)-cage: the Petersen graph, 10 vertices