Fair dissections of spiders, worms, and caterpillars

In the present paper we deal with equipartition problems for special classes of trees, i. e., spiders, stars, worms, and caterpillars. We prove that the equipartition problem is NP-complete for spiders (and, hence, for general trees); on the other hand, we give efficient polynomial-time algorithms for stars, worms, and caterpillars.