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Journal article
Completing Partial Latin Squares with Blocks of Non-empty Cells
Graphs and combinatorics, Vol.32(1), pp.241-256
01/01/2016
Web of Science ID: WOS:000367333000018
Abstract
In this paper we develop two methods for completing partial latin squares and prove the following. Let be a partial latin square of order in which all non-empty cells occur in at most squares. If are positive integers for which and if is the union of subsquares each with order , then can be completed. We additionally show that if and is the union of identical squares with disjoint rows and columns, then can be completed. For smaller values of we show that a completion does not always exist.
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Details
- Title
- Completing Partial Latin Squares with Blocks of Non-empty Cells
- Publication Details
- Graphs and combinatorics, Vol.32(1), pp.241-256
- Resource Type
- Journal article
- Publisher
- Springer Nature
- Copyright
- © 2015, Springer Japan
- Identifiers
- WOS:000367333000018; 99380182189706600
- Academic Unit
- Hal Marcus College of Science and Engineering ; Mathematics and Statistics
- Language
- English