Covering a Tree by a Forest

Authors:
Fanica Gavril;Alon Itai
Affiliations:
Department of Computer Science, Technion - IIT, Haifa, Israel;Department of Computer Science, Technion - IIT, Haifa, Israel
Venue:
Graph Theory, Computational Intelligence and Thought
Year:
2009

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Abstract

Consider a tree T and a forest F . The paper discusses the following new problems: The Forest vertex-cover problem (FVC) : cover the vertices of T by a minimum number of copies of trees of F , such that every vertex of T is covered exactly once. TheForest edge-cover problem (FEC) : cover the edges of T by a minimum number of copies of trees of F , such that every edge of T is covered exactly once. For a solution to always exist, we assume that F contains a one vertex (one edge) tree. Two versions of Problem FVC are considered: ordered covers (OFVC), and unordered covers (UFVC). Three versions of Problem FEC are considered: ordered covers (OFEC), unordered covers (UFEC) and consecutive covers (CFEC). We describe polynomial time algorithms for Problems OFVC, UFVC and CFEC, and prove that Problems OFEC and UFEC are NP-complete.