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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}
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]
The monochromatic triangle problem takes as input an n-node undirected graph G(V,E) with node set V and edge set E. The output is a Boolean value, true if the edge set E of G can be partitioned into two disjoint sets E1 and E2, such that both of the two subgraphs G1(V,E1) and G2(V,E2) are triangle-free graphs, and false otherwise.
Project row points onto the line connecting the origin and the standard coordinate of a column; if the projected position along that connection line is close to the position of the standard coordinate, that row point is strongly associated with this column i.e. in case of count data the row has a high frequency of that category and in case of ...
When a set S i that has already been chosen is split by a refinement, only one of the two resulting sets (the smaller of the two) needs to be chosen again; in this way, each state participates in the sets X for O(s log n) refinement steps and the overall algorithm takes time O(ns log n), where n is the number of initial states and s is the size ...
Social Security is the U.S. government's biggest program; as of June 30, 2024, about 67.9 million people, or one in five Americans, collected Social Security benefits. This year, we're seeing a...
Notre Dame has a postseason win over Georgia. And it can thank a one-minute stretch over the second and third quarters for the victory. The No. 7 Fighting Irish scored 17 points in 54 seconds ...
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 ...