2 problems

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Evans's completion conjecture for partial Latin squares
Evans's conjecture. Any partial Latin square of order $n$ with at most $n-1$ non-empty cells is completable.
Conjecturesolvedcombinatorics completion-problems latin-squaresarXiv posted 2 days ago
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Daykin–Häggkvist conjecture on completion of dense partial Latin squares
Daykin and Häggkvist's conjecture. Every $\frac{1}{4}$ -dense partial Latin square is completable.
Conjecturesolvedcombinatorics completion-problems latin-squaresarXiv posted 2 days ago

Evans's completion conjecture for partial Latin squares