On the Chudnovsky-Seymour-Sullivan conjecture on cycles in triangle-free digraphs
نویسندگان
چکیده
For a simple digraph G without directed triangles or digons, let β(G) be the size of the smallest subset X ⊆ E(G) such that G \ X has no directed cycles, and let γ(G) be the number of unordered pairs of nonadjacent vertices in G. In 2008, Chudnovsky, Seymour, and Sullivan showed that β(G) ≤ γ(G), and conjectured that β(G) ≤ γ(G)/2. Recently, Dunkum, Hamburger, and Pór proved that β(G) ≤ 0.88γ(G). In this note, we prove that β(G) ≤ 0.8616γ(G).
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