Long paths and Hamiltonicity in random graphs

TL;DR

This paper reviews classical results on long paths and Hamilton cycles in random graphs, providing accessible proofs using DFS and boosters to enhance understanding of these fundamental graph properties.

Contribution

It offers simplified, accessible proofs of key results on Hamiltonicity in random graphs using DFS and booster concepts.

Findings

Classical results on long paths in random graphs

Accessible proofs of Hamiltonicity using DFS

Introduction of boosters for graph connectivity

Abstract

We discuss several classical results about long paths and Hamilton cycles in random graphs and present accessible versions of their proofs, relying on the Depth First Search (DFS) algorithm and the notion of boosters.