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alpha_acyclic (775B)

      1 # Alpha acyclic
      2 
      3 Condition on [hypergraph]
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      5 On [graph_undirected], equivalent to [graph_acyclic]
      6 
      7 Equivalent to [running_intersection_property]
      8 
      9 Equivalent to having a [join_tree]
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     11 Equivalent to being both [hypergraph_conformal] and [hypergraph_chordal]
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     13 Equivalent to having an [alpha_elimination_order]
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     15 Equivalent to [querywidth] and [hypertreewidth] and [generalized_hypertreewidth] being 1
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     17 Defining paper proving the equivalences: [beeri1983desirability]
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     19 Can be checked on [hypergraph_reduced], i.e., hyperedges that are covered by another hyperedge do not matter
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     21 Can be tested in [linear_time] using [tarjan1984simple] via [chordal] and [hypergraph_chordal], but non-obvious
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     23 Up: [degree_of_acyclicity]
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     25 See also: [acyclic_hypergraph_sandwich_problem], [alpha_leaf]