Geodesic
Covering Problem for Idempotent Latin Squares
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 144-148

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Let A = (a ij ) be an idempotent latin square of order n, n ≥ 3, in which a ii = i, 1 ≤ i ≤ nc. A set S ⊆ N = {1, 2, ..., n} is a cover of A if (N × N)\{(i, i):i ∉ S} = {(i, j): i ∊ S, j ∊ N} ∪ {(j, i): i ∊ S, j ∊ N} ∪ {(i, j): a ij ∊ S}. A cover S is minimum for A if |S| < |T| for every cover T of A and we write c(A) = |S|. We denote by c(n) the maximum value of c(A) over all idempotent latin squares A of order n and in this paper show that (7n/10)-3.8 ≤ c (n) < n - n 1/3 + 1 for all n ≥ 15. The problem of determining c(n) was first raised by J. Schönheim.
DOI : 10.4153/CMB-1983-023-7
Mots-clés : 05B15 
Heinrich, Katherine. Covering Problem for Idempotent Latin Squares. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 144-148. doi: 10.4153/CMB-1983-023-7
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     title = {Covering {Problem} for {Idempotent} {Latin} {Squares}},
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     year = {1983},
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     doi = {10.4153/CMB-1983-023-7},
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