Document Type
Article
Publication Date
4-29-2016
Abstract
Let r,c,s ∈{1,2,…,n} and let PP 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 ∉ {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.
Recommended Citation
Kuhl J, Schroeder MW, Completing partial latin squares with one nonempty row, column, and symbol, The Electronic Journal of Combinatorics 23(2) (2016), #P2.23
Comments
Copyright © 2016 The Authors.
The copy of record is available from the publisher at https://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p23.