hypergraph_balanced (641B)
1 # Hypergraph balanced 2 3 A [hypergraph] is *balanced* if the following holds: for any [induced_subhypergraph], removing the [singleton] [hyperedges], we can 2-color the [vertices] such that there is no monochromatic [hyperedge] 4 5 - equivalent definition via [Berge_cycle]: every [Berge_cycle] of odd length contains a [hyperedge] containing at least three [vertices] of the cycle (like a [chord]) 6 7 Connection to [strongly_unimodular] [matrices] and [integer_linear_programming] 8 9 Notion of [hypergraph_strongly_balanced] in [crama1986strong], equivalent to [strongly_unimodular] 10 11 Up: [hypergraph] 12 13 See also: [graph_bipartite], [koenig_property]