Maximum chordal subgraphs of random graphs

TL;DR

This paper investigates the asymptotic size of the largest chordal subgraph in random graphs, providing new insights into its behavior across different probability regimes.

Contribution

It derives asymptotic results for the maximum size of chordal subgraphs in binomial random graphs for constant and polynomially decreasing edge probabilities.

Findings

Asymptotic formulas for constant p

Results for p = n^{-eta} with eta > 0

Enhanced understanding of chordal subgraph structure in random graphs

Abstract

We find asymptotics of the maximum size of a chordal subgraph in a binomial random graph $G(n,p)$, for $p=\mathrm{const}$ and $p=n^{-\alpha+o(1)}$.