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- W266618170 abstract "A Latin rectangle is an m × n matrix in which the entries of each row and each column are all distinct numbers. In a row-Latin rectangle only the rows are required to consist of distinct entries. A partial transversal in a Latin rectangle is a set of distinct numbers such that no two of them are in the same row or column. A well-known conjecture of Ryser, Brualdi and Stein [2,8] asserts that every n × n Latin rectangle has a partial transversal of size n − 1. Woolbright [9], and independently and Brouwer, de Vries and Wieringa [1], proved the existence of a partial transversal of size % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiabgk % HiTmaakaaabaGaamOBaaWcbeaaaaa!38DB! $$ n - sqrt n $$ and Shor and Hatami [5,7] improved the bound to n – O (log2 n)." @default.
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- W266618170 date "2013-01-01" @default.
- W266618170 modified "2023-09-27" @default.
- W266618170 title "On independent transversals in matroidal Latin rectangles" @default.
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- W266618170 doi "https://doi.org/10.1007/978-88-7642-475-5_86" @default.
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