Completing simple partial k-Latin squares

Authors

DOI:

https://doi.org/10.1478/AAPP.96S2A4

Keywords:

Simple k-Factorization, k-Factor, f-Factor, Multi-Latin Square, k- Latin Square, Completion, Generalized Latin Rectangles

Abstract

We study the completion problem for simple k-Latin rectangles, which are a special case of the generalized latin rectangles studied for which embedding theorems are given by Andersen and Hilton (1980) in “Generalized Latin rectangles II: Embedding”, Discrete Mathematics 31(3). Here an  alternative proof of those theorems are given for k-Latin rectangles in  the “simple” case. More precisely, generalizing two classic results on the  completability of partial Latin squares, we prove the necessary and suffisucient conditions for a completion of a simple m x n k-Latin rectangle to a simple k-Latin square of order n and we show that if m ≤ n/2, any simple partial k-Latin square P of order m embeds in a simple k-Latin square L of order n.

Author Biographies

  • Nicholas Cavenagh, University of Waikato
    Department of Mathematics
  • Giovanni Lo Faro, Università degli Studi di Messina
    Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra
  • Antoinette Tripodi, Università degli Studi di Messina
    Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra

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Published

2018-11-20

Issue

Vol 96, SUPPL NO 2 (2018): HyGraDe 2017

Section

HyGraDe 2017 (Conference Proceedings)

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