Every Strong Digraph has a Spanning Strong Subgraph with at most n + 2 α − 2 arcs
نویسندگان
چکیده
Answering a question of Adrian Bondy [4], we prove that every strong digraph has a spanning strong subgraph with at most n + 2α − 2 arcs, where α is the size of a maximum stable set of D. Such a spanning subgraph can be found in polynomial time. An infinite family of oriented graphs for which this bound is sharp was given by Odile Favaron [3]. A direct corollary of our result is that there exists 2α − 1 directed cycles which span D. Tibor Gallai [6] conjectured that α directed cycles would be enough.
منابع مشابه
The minimum spanning strong subdigraph problem is fixed parameter tractable
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