Journal of Combinatorial Optimization

, Volume 24, Issue 2, pp 67–98 | Cite as

A rooted-forest partition with uniform vertex demand

  • Naoki Katoh
  • Shin-ichi Tanigawa


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 .


Rooted-forest partition Tree-packing Matroids 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Architecture and Architectural EngineeringKyoto UniversityKyotoJapan
  2. 2.Research Institute for Mathematical ScienceKyoto UniversityKyotoJapan

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