A rooted-forest partition with uniform vertex demand
A rooted-forest is the union of vertex-disjoint rooted-trees. Suppose we are given a graph G=(V,E), a collection {R (1),aEuro broken vertical bar,R (k) } of k root-sets (i.e., vertex-sets), and a positive integer d. We prove a necessary and sufficient condition for G to contain k edge-disjoint rooted-forests F (1),aEuro broken vertical bar,F (k) with root-sets R (1),aEuro broken vertical bar,R (k) such that each vertex is spanned by exactly d of F (1),aEuro broken vertical bar,F (k) .
rooted-forest partition tree-packing matroids