Destroying cycles in digraphs
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AbstractFor a simple directed graph G with no directed triangles, 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) denote the number of unordered pairs of nonadjacent vertices in G. Chudnovsky, Seymour, and Sullivan showed that β(G) ≤ γ(G), and conjectured that β(G) ≤ $\tfrac{{\gamma (G)}}
{2}$
. In this paper we prove that β(G)<0.88γ(G).
[1] Benny Sudakov,et al. Directed Graphs Without Short Cycles , 2008, Combinatorics, Probability and Computing.
[2] Paul D. Seymour,et al. Cycles in dense digraphs , 2008, Comb..
[3] Alexandr V. Kostochka,et al. On Directed Triangles in Digraphs , 2007, Electron. J. Comb..