Hoàng–Reed conjecture holds for tournaments

Hoàng–Reed conjecture asserts that every digraph DD has a collection CC of circuits C1,…,Cδ+C1,…,Cδ+, where δ+δ+ is the minimum outdegree of DD, such that the circuits of CC have a forest-like structure. Formally, |V(Ci)∩(V(C1)∪⋯∪V(Ci-1))|⩽1|V(Ci)∩(V(C1)∪⋯∪V(Ci-1))|⩽1, for all i=2,…,δ+i=2,…,δ+. We verify this conjecture for the class of tournaments.