Perfect matchings and loose Hamilton cycles in the semirandom hypergraph model

Molloy, Michael, Pralat, Pawel and Sorkin, Gregory B. ORCID: 0000-0003-4935-7820 (2025) Perfect matchings and loose Hamilton cycles in the semirandom hypergraph model. Random Structures and Algorithms, 66 (2). ISSN 1042-9832

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Abstract

We study the 2-offer semirandom 3-uniform hypergraph model on n vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching, and another that constructs a loose Hamilton cycle, both succeeding asymptotically almost surely within Θ(n) steps. Both results extend to s-uniform hypergraphs. Our methods are qualitatively different from those that have been used for semirandom graphs. Much of the analysis is done on an auxiliary graph that is a uniform k-out subgraph of a random bipartite graph, and this tool may be useful in other contexts.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	30 Oct 2024 15:06
Last Modified:	04 Nov 2025 01:13
URI:	http://eprints.lse.ac.uk/id/eprint/125930

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