On Finding Acyclic Subhypergraphs

: In this paper, we investigate the problem to find an acyclic subhypergraph in a given hypergraph, which is an extension to find a tree in a graph. First, we introduce a spanning acyclic subhypergraph, as an extension of a spanning tree. We say that an acyclic subhypergraph H of a hypergraph H is spanning if for every vertex v in H there exists a hyperedge E in H such that v ∈ E. Then, we show that the problem of determining whether or not a hypergraph has a spanning acyclic subhypergraph is NPcomplete. Next, instead of the spanning acyclic subhypergraph, we introduce a maximal acyclic subhypergraph, which is an acyclic subhypergraph that is cyclic if we add any hyperedge of the original hypergraph to it. Then, we design the algorithm mas to find it, which is based on acyclicity test algorithm by Tarjan and Yannakakis (1984). 

• Type: Conference
• Year: 2005
• Where: FCT
• Authors: Kouichi Hirata, Megumi Kuwabara, Masateru Harao
• Keywords: Acyclic Subhypergraph, FCT 2005, Maximal Acyclic Subhypergraph, Spanning Tree