Splitting a tournament into two subtournaments with given minimum outdegree
نویسندگان
چکیده
A (k1, k2)-outdegree-splitting of a digraph D is a partition (V1, V2) of its vertex set such that D[V1] and D[V2] have minimum outdegree at least k1 and k2, respectively. We show that there exists a minimum function fT such that every tournament of minimum outdegree at least fT (k1, k2) has a (k1, k2)outdegree-splitting, and fT (k1, k2) ≤ k 1/2+3k1/2+k2+1. We also show a polynomial-time algorithm that finds a (k1, k2)-outdegree-splitting of a tournament if one exists, and returns ‘no’ otherwise. We give better bound on fT and faster algorithms when k1 = 1.
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