Partial Chromatic Polynomials and Diagonally Distinct Sudoku Squares

Details Partial Chromatic Polynomials and Diagonally Distinct Sudoku Squares Partial Chromatic Polynomials and Diagonally Distinct Sudoku Squares

2008-04-02

arxiv.org/abs/0804.0284v2

Mathematics

Combinatorics

5 pages. Expanded by adding a new proof of a theorem on partial colorings. We also acknowledge an earlier proof of the diagona

Scientific paper

Sudoku grids can be thought of as graphs where the vertices are the squares of the grid, and edges join vertices in the same row, column, or sub-grid. A Sudoku puzzle corresponds to a partial proper coloring of the Sudoku graph. We provide a new and simpler proof of the theorem which states that the number of completions of partial colorings of a graph is a polynomial in the number of colors (originally due to Herzberg and Murty). Moreover, we construct Sudoku squares of arbitrary size with distinct entries on both diagonals (a similar proof was first published by Keedwell, unknown to the author).

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