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arXiv · 2608.24520

Homomorphic-core phase transition threshold in Erdős--Rényi random graphs

Jiaheng Wang
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Abstract

It is shown in this manuscript that a random graph $G$ drawn from the Erdős--Rényi model $\mathcal{G}(n,p)$ with \[ p=p(n)\leq 1/2, \qquad \lim_{n\to+\infty}(np-\log n-\log\log n)=+\infty, \] is a homomorphic core, i.e., every homomorphism from $G$ to itself is an automorphism. This implies tight ETH-based lower bounds of the subgraph isomorphism problem for almost all $k$-vertex patterns with polynomial average degree.

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Jiaheng Wang. 2026-08-25. Homomorphic-core phase transition threshold in Erdős--Rényi random graphs. https://arxiv.org/abs/2608.24520

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