Globally balancing spanning trees

We show that for every graph G contains two edge-disjoint spanning trees, we can choose trees T1,T2 of such |dT1(v)−dT2(v)|≤5 all v∈V(G). also prove the more general statement positive integer k, there is a constant ck∈O(logk) k T1,…,Tk satisfying |dTi(v)−dTj(v)|≤ck v∈V(G) and i,j∈{1,…,k}. This resolves conjecture Kriesell.