A step towards the Bermond-Thomassen conjecture about disjoint cycles in digraphs
نویسندگان
چکیده
In 1981, Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k − 1 contains k disjoint cycles. This conjecture is trivial for k = 1, and was established for k = 2 by Thomassen in 1983. We verify it for the next case, by proving that every digraph with minimum out-degree at least five contains three disjoint cycles. To show this, we improve Thomassen’s result by proving that every digraph whose vertices have out-degree at least three, except at most two with out-degree two, indeed contains two disjoint cycles.
منابع مشابه
A Step toward the Bermond--Thomassen Conjecture about Disjoint Cycles in Digraphs
In 1981, Bermond and Thomassen conjectured that every digraph with minimum out-degree at least 2k − 1 contains k disjoint cycles. This conjecture is trivial for k = 1, and was established for k = 2 by Thomassen in 1983. We verify it for the next case, by proving that every digraph with minimum out-degree at least five contains three disjoint cycles. To show this, we improve Thomassen’s result b...
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