LIPIcs - Leibniz International Proceedings in Informatics. 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Doi
Abstract
Specialized hereditary systems, e.g., matroids, are known to have many applications in algorithm design. We define a new notion called d-polynomoid as a hereditary system (E, ? ? 2^E) so that every two maximal sets in ? have less than d elements in common. We study the problem that, given a d-polynomoid (E, ?), asks if the ground set E contains ? disjoint k-subsets that are not in ?, and obtain a complexity trichotomy result for all pairs of k ? 1 and d ? 0. Our algorithmic result yields a sufficient and necessary condition that decides whether each hypergraph in some classes of r-uniform hypergraphs has a perfect matching, which has a number of algorithmic applications