Total domination and least domination in a tree

The total domination number γt of a graph G=(V,E) is the minimum cardinality of a dominating set D of G such that every vertex of V has at least one neighbor in D. The least domination number γL of G is the minimum cardinality of a dominating set X of G whose domination number is the minimum. In this paper, we prove the following conjecture due to Odile Favaron: Conjecture. For any tree T, we have γL(T)/γt(T)⩽3/2.