Abstract
In this paper, we investigate the problem of finding acyclic subhypergraphs in a hypergraph. First we show that the problem of determining whether or not a hypergraph has a spanning connected acyclic subhypergraph is NP-complete. Also we show that, for a given K > 0, the problem of determining whether or not a hypergraph has an acyclic subhypergraph containing at least K hyperedges is NP-complete. Next, 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 linear-time algorithm mas to find it, which is based on the acyclicity test algorithm designed by Tarjan and Yannakakis (1984).
This work is partially supported by Grand-in-Aid for Scientific Research 15700137 and 16016275 from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
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Hirata, K., Kuwabara, M., Harao, M. (2005). On Finding Acyclic Subhypergraphs. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_43
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DOI: https://doi.org/10.1007/11537311_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28193-1
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