2 problems

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Sparse partial Latin rectangle containment conjecture
For $K>0$ , a $k\times n$ Latin rectangle is $K$ -sparse if every row contains at most $K$ non-empty cells, every column contains at most $K$ non-empty cells, and every symbol occurs…
Conjecturesolvedlatin-rectangles partial-latin-squares random-structuresarXiv posted 2 days ago
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Kuhl–McGinn's completion conjecture for partial Latin squares with two rows and three columns
Kuhl–McGinn's conjecture. Every partial Latin square of order $n\geq 8$ with two completely filled rows and three completely filled columns, and with all other cells empty, is comp…
Conjecturesolvedcombinatorics latin-squares partial-latin-squaresarXiv posted 2 days ago

Sparse partial Latin rectangle containment conjecture