Spread blow-up lemma with an application to perturbed random graphs
<|reference_start|>Spread blow-up lemma with an application to perturbed random graphs: Combining ideas of Pham, Sah, Sawhney, and Simkin on spread perfect matchings in super-regular bipartite graphs with an algorithmic blow-up lemma, we prove a spread version of the blow-up lemma. Intuitively, this means that there exists a probability measure over copies of a desired spanning graph $H$ in a given system of super-regular pairs which does not heavily pin down any subset of vertices. This allows one to complement the use of the blow-up lemma with the recently resolved Kahn-Kalai conjecture. As an application, we prove an approximate version of a conjecture of B\"ottcher, Parczyk, Sgueglia, and Skokan on the threshold for appearance of powers of Hamilton cycles in perturbed random graphs.<|reference_end|>
@article{nenadov2024spread,
    title={Spread blow-up lemma with an application to perturbed random graphs},
    author={Rajko Nenadov, Huy Tuan Pham},
    journal={arXiv preprint arXiv:2410.06132},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.06132},
    primaryClass={math.CO cs.DM math.PR}
}