Document Type
Article
Publication Title
Journal of Combinatorial Designs
Publication Date
2025
Keywords
(g f)-factors, completion, Hall's theorem, multi-Latin squares, partial
Abstract
Let Q be an n x n array whose top left r x s sub‐array L is filled with a set of k different symbols such that each cell of L contains λ symbols. In this note, we find conditions under which each empty cell of Q can be filled with λ symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol
occurs at most λ times in each row and column of Q. To prove this result, we establish a new criterion for a bipartite graph to have a subgraph with prescribed degree conditions. Our proof is self‐contained and relies on the alternating path technique.
Funding Source
This article was published Open Access thanks to a transformative agreement between Milner Library and Wiley.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
DOI
10.1002/jcd.22008
Recommended Citation
Bahmanian, A. 2025. “ Completing Multi-Latin Rectangles via Factors with Prescribed Degrees in Bipartite Graphs.” J. Combin. Des. 1–6. https://doi.org/10.1002/jcd.22008
Comments
First published in Journal of Combinatorial Designs (2025): https://doi.org/10.1002/jcd.22008