# BF-graph

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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-arc. 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.

## References

• G. Gallo, G.Longo, S. Nguyen and S. Pallottino (1993). Directed hypergraphs and applications. Discrete Applied Mathematics 42 (2-3). pp. 177–201.
• S. Nguyen, D. Pretolani and L. Markenson (1998). On Some Path Problems on Oriented Hypergraphs. ITA 32 (1-3). pp. 1–20.