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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]
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.
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 ...
A stronger definition of bipartiteness is: a hypergraph is called bipartite if its vertex set V can be partitioned into two sets, X and Y, such that each hyperedge contains exactly one element of X. [2] [3] Every bipartite graph is also a bipartite hypergraph. Every bipartite hypergraph is 2-colorable, but bipartiteness is stronger than 2 ...
The Golden State Warriors lost their NBA Cup game against the Denver Nuggets 119-115 on Tuesday night, and head coach Steve Kerr was not happy with the way it ended.
Bread, Friedlander also said, is "built into" his restaurant's model. One restaurateur told Fox News Digital he would be "flattered" if someone took home the complimentary bread from the table ...
A man is being held without bail for allegedly stabbing three of his family members to death, including an 8-year-old girl and teenage boy, Los Angeles County District Attorney Nathan Hochman ...