The outerplanar Turán number of disjoint copies of paths

Abstract

A graph without a copy of T as a subgraph is called T-free. The outerplanar Turán number $e{x}_{{}_{OP}}(n,T)$ of T represents the maximum number of edges among all n-vertex T-free outerplanar graphs. In this paper, we investigate $e{x}_{{}_{OP}}(n,r{P}_s)$ and determine its exact value for $r,s\ge 2$ and $n\ge rs$. This extends a result of Fang and Zhai (2023) [7].