Add to ORKGIn 1975 Stein conjectured that in every n × n array filled with the numbers 1,...,n with every number occuring exactly n times, there is a partial transversal of size n − 1. In this note we show that this conjecture is false by constructing such arrays without partial transverals of size n−(1/42)ln(n)
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
Linial and Morgenstern conjectured that, among all n-vertex tournaments with cycles of length three...
AbstractThe notion of partial transversal in a Latin square is defined. A proof is given of the exis...
In 1975 Stein conjectured that in every n × n array filled with the numbers 1, . . . , n with every...
In 1975 Stein conjectured that in every n×n array filled with the numbers 1,…,n with every number oc...
AbstractIt is proved that every n×n Latin square has a partial transversal of length at least n−O(lo...
AbstractIn this paper it is shown that every m×n array in which each symbol appears at most (mn-1)/(...
AbstractIt is proved that every n × n Latin square has a partial transversal of length at least n − ...
AbstractWe investigate transversals of rectangular arrays. For positive integers m and n, where 2⩽m⩽...
The full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we...
Aharoni and Berger conjectured that every collection of n matchings of size n+1 in a bipartite grap...
AbstractIt is well known that if n is even, the addition table for the integers modulo n (which we d...
A Latin square is reduced if its first row and column are in natural order. For Latin squares of a p...
A “Latin square of order n” is an “n by n” array of the symbols 1, 2, ... , n, such that each symbol...
A latin square of order n is an n by n array whose entries are drawn from an n-set of symbols such t...
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
Linial and Morgenstern conjectured that, among all n-vertex tournaments with cycles of length three...
AbstractThe notion of partial transversal in a Latin square is defined. A proof is given of the exis...
In 1975 Stein conjectured that in every n × n array filled with the numbers 1, . . . , n with every...
In 1975 Stein conjectured that in every n×n array filled with the numbers 1,…,n with every number oc...
AbstractIt is proved that every n×n Latin square has a partial transversal of length at least n−O(lo...
AbstractIn this paper it is shown that every m×n array in which each symbol appears at most (mn-1)/(...
AbstractIt is proved that every n × n Latin square has a partial transversal of length at least n − ...
AbstractWe investigate transversals of rectangular arrays. For positive integers m and n, where 2⩽m⩽...
The full n-Latin square is the n×n array with symbols 1, 2, . . . , n in each cell. In this paper we...
Aharoni and Berger conjectured that every collection of n matchings of size n+1 in a bipartite grap...
AbstractIt is well known that if n is even, the addition table for the integers modulo n (which we d...
A Latin square is reduced if its first row and column are in natural order. For Latin squares of a p...
A “Latin square of order n” is an “n by n” array of the symbols 1, 2, ... , n, such that each symbol...
A latin square of order n is an n by n array whose entries are drawn from an n-set of symbols such t...
A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of ...
Linial and Morgenstern conjectured that, among all n-vertex tournaments with cycles of length three...
AbstractThe notion of partial transversal in a Latin square is defined. A proof is given of the exis...