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The subset of edges that have one endpoint in each side is called a cut-set. When a cut-set forms a complete bipartite graph, its cut is called a split. Thus, a split can be described as a partition of the vertices of the graph into two subsets X and Y, such that every neighbor of X in Y is adjacent to every neighbor of Y in X. [2]
An example of a maximum cut. In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary sets S and T, such that the number of edges between S and T is as large as possible.
A split graph may have more than one partition into a clique and an independent set; for instance, the path a–b–c is a split graph, the vertices of which can be partitioned in three different ways: the clique {a, b} and the independent set {c} the clique {b, c} and the independent set {a} the clique {b} and the independent set {a, c}
A cut C = (S, T) is a partition of V of a graph G = (V, E) into two subsets S and T. The cut-set of a cut C = (S, T) is the set {(u, v) ∈ E | u ∈ S, v ∈ T} of edges that have one endpoint in S and the other endpoint in T. If s and t are specified vertices of the graph G, then an s – t cut is a cut in which s belongs to the set S and t ...
In computational complexity theory, the set splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S 1, S 2 such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S 1 or S 2.
Coach Prime took a 1-11 team with virtually no recent success and turned them into winners in just two years without crisscrossing the country recruiting high school players. There is no reason to ...
The two No. 1's are the only teams that get a first-round bye in the playoffs, while every other playoff team must battle it out to make it to the next week. There's an interesting situation ...
Beck missed the second half of the game, and backup quarterback Gunner Stockton took over and led the Bulldogs to the win in overtime. That secured them a spot in the College Football Playoff and ...