A rooted-forest partition with uniform vertex demand

Authors:
Naoki Katoh;Shin-Ichi Tanigawa
Affiliations:
Department of Architecture and Architectural Engineering, Kyoto University, Kyoto, Japan;Research Institute for Mathematical Science, Kyoto University, Kyoto, Japan
Venue:
Journal of Combinatorial Optimization
Year:
2012

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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,驴,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,驴,F k with root-sets R 1,驴,R k such that each vertex is spanned by exactly d of F 1,驴,F k .