Pendant appearances and components in random graphs from structured classes

TL;DR

This paper studies the properties of random graphs from structured classes, focusing on pendant appearances and component distributions, providing sharper results and broader applicability than previous work.

Contribution

It extends and refines earlier results on pendant appearances and asymptotic component distributions in structured random graphs.

Findings

Sharper bounds on pendant appearances like leaves.

Asymptotic distribution results for non-giant components.

Applicability to graphs embeddable in surfaces.

Abstract

We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of leaves; and obtain results on the asymptotic distribution of components other than the giant component, under quite general conditions.