, B i?3, vol.1

, For small cases, we can provide better bounds

, So h(1) = 1. If ? > 1, we first apply Proposition 8.3 to find an acyclic dominating set A of D. Then we apply Proposition 6.16 to find a dominating set S ? A of A. Note that |S| ? since S is stable, There is an integer such that for every positive integer ?, if D is an ?-dense C 3 -free digraph, then D has a dominating set of size ? . that ?(D) h(?)

, We partition Y into |S| subsets, where for each s ? S, Y s is a subset of N o (s)

, Observe that Y = s?S Y s is dominated by s?S B s , and V \ Y is dominated by S by definition of Y. Thus, B is a dominating set of D

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