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Journal of Combinatorics
Volume 12 (2021)
Number 4
Random graphs induced by Catalan pairs
Pages: 663 – 724
DOI: https://dx.doi.org/10.4310/JOC.2021.v12.n4.a5
Authors
Abstract
We consider Catalan-pair graphs, a family of graphs that can be viewed as representing certain interactions between pairs of objects which are enumerated by the Catalan numbers. In this paper we study random Catalan-pair graphs and deduce various properties of these random graphs. In particular, we asymptotically determine the expected number of edges and isolated vertices, and more generally we determine the expected number of (induced) subgraphs isomorphic to a given connected graph.
Keywords
Catalan number, random graphs, circle graphs
Received 5 March 2020
Accepted 15 September 2020
Published 31 January 2022