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The conjecture on cycle-free partial transversals of Latin squares
A Latin square of order $n$ is an $n\times n$ array in which every symbol occurs exactly once in each row and column. A cycle-free partial transversal is a partial transversal cont…
Conjectureopencombinatorics latin-squares partial-transversalsarXiv posted 2 days ago
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Generalized Brualdi conjecture on partial k-plexes in latin squares
Generalized Brualdi conjecture. Every latin square of order $n$ has a partial $k$ -plex of order $k(n-k)$ for each $k\le n$ .
Conjectureopenlatin-squares partial-transversalsarXiv posted 2 days ago

The conjecture on cycle-free partial transversals of Latin squares