Destroying cycles in digraphs

Abstract

For a simple directed graph G with no directed triangles, let β(G) be the size of the smallest subset XE(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).

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Correspondence to Molly Dunkum.

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Dunkum, M., Hamburger, P. & Pór, A. Destroying cycles in digraphs. Combinatorica 31, 55 (2011). https://doi.org/10.1007/s00493-011-2589-4

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Mathematics Subject Classification (2000)

  • 05C20
  • 05C38
  • 05C85