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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]
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}
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 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 ...
A complete bipartite graph with m = 5 and n = 3 The Heawood graph is bipartite.. In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in .
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 ...
With Christmas near, bringing out the boughs of holly now -- even as you may still be putting fall decorations away -- may make you a happier person, experts say. "For most people, decorating for ...
graph intersection: G 1 ∩ G 2 = (V 1 ∩ V 2, E 1 ∩ E 2); [1] graph join: . Graph with all the edges that connect the vertices of the first graph with the vertices of the second graph. It is a commutative operation (for unlabelled graphs); [2] graph products based on the cartesian product of the vertex sets:
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