Abstract
An ordered matching is an ordered graph which consists of vertex-disjoint edges (and have no isolated vertices). In this paper we focus on unavoidable patterns in such matchings. First, we investigate the size of canonical substructures in ordered matchings and generalize the Erdős-Szekeres theorem about monotone sequences. We also estimate the size of canonical substructures in a random ordered matching. Then we study twins, that is, pairs of order-isomorphic, disjoint sub-matchings. Among other results, we show that every ordered matching of size n contains twins of length Ω(n3 / 5), but the length of the longest twins in almost every ordered matching is O(n2 / 3).
Author supplied keywords
Cite
CITATION STYLE
Dudek, A., Grytczuk, J., & Ruciński, A. (2022). Patterns in Ordered (random) Matchings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13568 LNCS, pp. 544–556). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-20624-5_33
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
