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;Department of Architecture and Architectural Engineering, Kyoto University, Kyoto, Japan
Venue:
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Year:
2010

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Abstract

A rooted-forest is a graph having self-loops such that each connected component contains exactly one loop, which is regarded as a root, and there exists no cycle consisting of non-loop edges. In this paper, we shall study on a partition of a graph into edge-disjoint rooted-forests such that each vertex is spanned by exactly d components of the partition, where d is a positive integer.