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2842. A new class of premature, partial latin squares
Invited abstract in session TA-25: Applications of combinatorial optimization I, stream Combinatorial Optimization.
Tuesday, 8:30-10:00Room: 011 (building: 208)
Authors (first author is the speaker)
| 1. | Reinhardt Euler
|
| Lab-STICC UMR 6285 Université de Brest |
Abstract
A partial (i.e., partially filled) latin square PLS is called premature, if it is not completable to a full latin square (of the same order) but completable to such a latin square after deletion of any of its symbols. The complete knowledge of this kind of PLS would give an answer to the completability problem for latin squares in the following sense: a PLS can be completed if and only if it does not contain a premature PLS as a subsquare. One may also think of a hypergraph whose maximal independent sets are given by the full latin squares of a given order and whose hyperedges are to be described explicitly.
We survey some known examples for a premature PLS and present a new class obtained from a combination of two well-known types.
Keywords
- Combinatorial Optimization
- Graphs and Networks
Status: accepted
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