Hypergraphs | Families of sets

Property B

In mathematics, Property B is a certain set theoretic property. Formally, given a finite set X, a collection C of subsets of X has Property B if we can partition X into two disjoint subsets Y and Z such that every set in C meets both Y and Z. The property gets its name from mathematician Felix Bernstein, who first introduced the property in 1908. Property B is equivalent to 2-coloring the hypergraph described by the collection C. A hypergraph with property B is also called 2-colorable. Sometimes it is also called bipartite, by analogy to the bipartite graphs.Property B is often studied for uniform hypergraphs (set systems in which all subsets of the system have the same cardinality) but it has also been considered in the non-uniform case. The problem of checking whether a collection C has Property B is called the set splitting problem. (Wikipedia).

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Related pages

Set theory | Bipartite graph | Mathematics | Finite set | Set splitting problem | Hypergraph | Subset