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Matchings and Loose Cycles in the Semirandom Hypergraph Model

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  • UserGreg Sorkin (LSE)
  • ClockThursday 22 February 2024, 14:30-15:30
  • HouseMR12.

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The `semirandom graph process’, introduced in 2020, has attracted a good deal of study. I will discuss the 2-offer 3-uniform semirandom hypergraph model on $n$ vertices. Here, 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 $\Theta(n)$ steps. 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.

This talk is part of the Combinatorics Seminar series.

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