积分自由形式数独图

Q2 Mathematics

Electronic Notes in Discrete Mathematics Pub Date : 2018-07-01 DOI:10.1016/j.endm.2018.06.009

Omar Alomari, Mohammad Abudayah, Torsten Sander

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引用次数: 0

摘要

自由形式的数独谜题是m×m细胞的正方形排列，这些细胞被划分为m个基数相等的子集(称为块)。这个谜题的目标是在单元格中放置整数1，…m，这样每一行、每一列和每一块中的数字都是不同的。用一个顶点表示每个单元格，并在两个顶点之间添加边，当对应的单元格必须包含不同的数字时，根据规则。这将生成相关的自由格式数独图。证明了所有的数独图都是积分图，本文给出了许多仍然是积分图的自由形式数独图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Integral Free-Form Sudoku graphs

A free-form Sudoku puzzle is a square arrangement of $m \times m$ cells such that the cells are partitioned into m subsets (called blocks) of equal cardinality. The goal of the puzzle is to place integers $1, \dots m$ in the cells such that the numbers in every row, column and block are distinct. Represent each cell by a vertex and add edges between two vertices exactly when the corresponding cells, according to the rules, must contain different numbers. This yields the associated free-form Sudoku graph. It was shown that all Sudoku graphs are integral graphs, in this paper we present many free-form Sudoku graphs that are still integral graphs.

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来源期刊

Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.