Near-optimal induced universal graphs for cycles and paths

A graph U is an induced universal graph for a family F of graphs if every graph in F is a vertex-induced subgraph of U. Recently, for the family of all undirected graphs on n vertices, Alon [Geom. Funct. Anal. 2017] [3] proved the existence of an induced universal graph with (1+o(1))⋅2(n−1)∕2 vertices improving the previous best bound of 16⋅2n∕2 by Alstrup et al. (2015) and matching the lower bound of 2(n−1)∕2 by Moon (1965) up to lower order additive terms. We continue this line of research of finding the size of the smallest induced universal graph up to lower order additive terms for some basic graph families.