Abstract
A rooted-forest is the union of vertex-disjoint rooted-trees. Suppose we are given a graph G=(V,E), a collection {R 1,…,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,…,F k with root-sets R 1,…,R k such that each vertex is spanned by exactly d of F 1,…,F k .
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Katoh, N., Tanigawa, Si. A rooted-forest partition with uniform vertex demand. J Comb Optim 24, 67–98 (2012). https://doi.org/10.1007/s10878-010-9367-x
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DOI: https://doi.org/10.1007/s10878-010-9367-x