Covers and partial transversals of Latin squares
نویسندگان
چکیده
منابع مشابه
Rainbow matchings and partial transversals of Latin squares
In this paper we consider properly edge-colored graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A matching is called rainbow if its edges have different colors. The minimum degree of a graph is denoted by δ(G). We show that properly edge colored graphs G with |V (G)| ≥ 4δ(G) − 3 have rainbow matchings of size δ(G), this gives the best know...
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Author: Jenny Zhang First, let’s preview what mutually orthogonal Latin squares are. Two Latin squares L1 = [aij ] and L2 = [bij ] on symbols {1, 2, ...n}, are said to be orthogonal if every ordered pair of symbols occurs exactly once among the n2 pairs (aij , bij), 1 ≤ i ≤ n, 1 ≤ j ≤ n. Now, let me introduce a related concept which is called transversal. A transversal of a Latin square is a se...
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Let A = {a1, . . . , ak} and B = {b1, . . . , bk} be two subsets of an Abelian group G, k ≤ |G|. Snevily conjectured that, when G is of odd order, there is a permutation π ∈ Sk such that the sums ai+bπ(i), 1 ≤ i ≤ k, are pairwise different. Alon showed that the conjecture is true for groups of prime order, even when A is a sequence of k < |G| elements, i.e., by allowing repeated elements in A. ...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2018
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-018-0499-9