Trees with three leaves are (n + l)-unavoidable

We prove that every tree of order n 5 with three leaves is (n + 1)-unavoidable. More precisely, we prove that every tree A with three leaves of order n is contained in every tournament T of order n + 1 except if (T ; A) is (R 5 ; S + 3) or its dual, where R 5 is the regular tournament on ve vertices and S + 3 is the outstar of degree three, that is, the tree consisting of a root dominating three leaves. We then deduce that Sumner's conjecture is true for trees with four leaves, i.e. every tree of order n with four leaves is (2n ? 2)-unavoidable.