Pith. sign in

REVIEW

Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2212.06109 v2 pith:CLQRHU67 submitted 2022-12-12 math.CO cs.DMmath.PR

classification math.COcs.DMmath.PR
keywords latinrandomresultssteinersystemstripleaggkvistanalogous
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We show that the threshold for the binomial random $3$-partite, $3$-uniform hypergraph $G^{3}((n,n,n),p)$ to contain a Latin square is $\Theta(\log{n}/n)$. We also prove analogous results for Steiner triple systems and proper list edge-colorings of the complete (bipartite) graph with random lists. Our results answer several related questions of Johansson, Luria-Simkin, Casselgren-H\"aggkvist, Simkin, and Kang-Kelly-K\"uhn-Methuku-Osthus.

Discussion (0). Sign in to comment.

Pith tools