Completing partial Latin squares with one nonempty row, column, and symbol

Jaromy Kuhl¹ ; Michael W. Schroeder²

¹University of West Florida
²Marshall University

The electronic journal of combinatorics, Tome 23 (2016) no. 2

Résumé

Let $r,c,s\in\{1,2,\ldots,n\}$ and let $P$ be a partial latin square of order $n$ in which each nonempty cell lies in row $r$, column $c$, or contains symbol $s$. We show that if $n\notin\{3,4,5\}$ and row $r$, column $c$, and symbol $s$ can be completed in $P$, then a completion of $P$ exists. As a consequence, this proves a conjecture made by Casselgren and Häggkvist. Furthermore, we show exactly when row $r$, column $c$, and symbol $s$ can be completed.

Détail

DOI : 10.37236/5675

Classification : 05B15, 05A05
Mots-clés : partial Latin square, completing