Some problems in graph theory and graphs algorithmic theory

  title={Some problems in graph theory and graphs algorithmic theory},
  author={St{\'e}phane Bessy},
The Bermond-Thomassen conjecture states that, for any positive integer r, a digraph of minimum out-degree at least 2r − 1 contains at least r vertex-disjoint directed cycles. Thomassen proved that it is true when r = 2, and very recently the conjecture was proved for the case where r = 3. It is still open for larger values of r, even when restricted to (regular) tournaments. In this paper, we present two proofs of this conjecture for tournaments with minimum out-degree and minimum in-degree at… CONTINUE READING
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