2015/08/15 by Daniel Kotlar, Kotlar, Dani, Ziv Ran +1
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1508.03751
openalex publication_date 2015/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an n× n array M (n≥ 7), where each cell is colored in one of two colors, we give a necessary and sufficient condition for the existence of a partition of M into n diagonals, each containing at least one cell of each color. As a consequence, it follows that if each color appears in at least 2n-1 cells, then such a partition exists. The proof uses results on completion of partial Latin squares.