Random graphs induced by Catalan pairs

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

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Received 5 March 2020

Accepted 15 September 2020

Published 31 January 2022