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SUMMARY:Matchings and Loose Cycles in the Semirandom Hypergraph Model - Gr
 eg Sorkin (LSE) 
DTSTART:20240222T143000Z
DTEND:20240222T153000Z
UID:TALK212485@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:The `semirandom graph process'\, introduced in 2020\, has attr
 acted a\n   good deal of study. I will discuss the 2-offer 3-uniform semir
 andom\n   hypergraph model on $n$ vertices. Here\, at each step\, we are\n
    presented with 2 uniformly random vertices. We choose any other\n   ver
 tex\, thus creating a hyperedge of size 3. We show a strategy that\n   con
 structs a perfect matching\, and another that constructs a loose\n   Hamil
 ton cycle\, both succeeding asymptotically almost surely within\n   $\\The
 ta(n)$ steps. Our methods are qualitatively different from\n   those that 
 have been used for semirandom graphs. Much of the\n   analysis is done on 
 an auxiliary graph that is a uniform $k$-out\n   subgraph of a random bipa
 rtite graph\, and this tool may be useful in\n   other contexts.
LOCATION:MR12
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