Related necessary conditions for completing partial latin squares
نویسندگان
چکیده
منابع مشابه
Necessary Conditions for the Completion of Partial Latin Squares·
A latin square is an n x n square matrix each of which cells contains a symbol chosen from the set 11,2, ... ,n]; each symbol occurs exactly oncl~ in each row or column of the matrix. A partial latin square is a latin square in which some cells are unoccupied. We consider the problem of obtaining necessary and sufficient conditions for a partial latin square to be completed to a latin square. F...
متن کاملCompleting partial latin squares: Cropper's question
Hall’s condition is a well-known necessary condition for the existence of a proper coloring of a graph from prescribed lists. Completing a partial latin square is a very special kind of graph list-coloring problem. Cropper’s question was: is Hall’s condition sufficient for the existence of a completion of a partial latin square? The folk belief that the answer must be no is confirmed here, but,...
متن کاملCompleting partial latin squares with prescribed diagonals
This paper deals with completion of partial latin squares L = (lij) of order n with k cyclically generated diagonals (li+t,j+t = lij + t if lij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2, . . . , 7 and odd n ≤ 21, and we describe the computational method used (hill-climbing). Noncyclic completion is investigated ...
متن کاملOn Completing Latin Squares
We present a ( 2 3 − o(1))-approximation algorithm for the partial latin square extension (PLSE) problem. This improves the current best bound of 1− 1 e due to Gomes, Regis, and Shmoys [5]. We also show that PLSE is APX-hard. We then consider two new and natural variants of PLSE. In the first, there is an added restriction that at most k colors are to be used in the extension; for this problem,...
متن کاملCompleting Partial Latin Squares with Two Prescribed Diagonals
In the present paper we will prove that every partial latin square L = (lij) of odd order n with 2 cyclically generated diagonals (li+t,j+t = lij+t if lij is not empty; with calculations modulo n) can be cyclically completed.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1980
ISSN: 0097-3165
DOI: 10.1016/0097-3165(80)90044-8