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In graph theory, a BF-graph is a type of directed hypergraph where each hyperedge is directed either to one particular vertex or away from one particular vertex.

In a directed hypergraph, each hyperedge may be directed away from some of its vertices (its tails) and towards some others of its vertices (its heads). A hyperedge that is directed to a single head vertex, and away from all its other vertices, is called a B-arch. Symmetrically, a hyperedge that is directed away from a single tail vertex, and towards all its other vertices, is called an F-arc.

If a hypergraph has only B-arcs, it is called a B-graph. If a hypergraph has only F-arcs, it is called an F-graph.yperarc with a tail of size 1. A hypergraph with only B-arcs is a B-graph and a hypergraph with only F-arcs is a F-graph.


  • G. Gallo; G.Longo; S. Nguyen & S. Pallottino (1993). Directed hypergraphs and applications. Discrete Applied Mathematics. 42. pp. 177–201. 
  • S. Nguyen; D. Pretolani & L. Markenson (1998). On Some Path Problems on Oriented Hypergraphs. ITA. 32. pp. 1–20.