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A note on directed 4-cycles in digraphs
Using some combinatorial techniques, in this note, it is proved that if
, then any digraph on vertices with minimum outdegree
at least contains a directed cycle of length at most 4
On the minimal feedback arc set of m-free Digraphs
For a simple digraph , let be the size of the smallest subset
such that has no directed cycles, and let
be the number of unordered pairs of nonadjacent vertices in . A digraph
is called -free if has no directed cycles of length at most . This
paper proves that for any -free
digraph , which generalized some known results
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