论文标题
Sudoku编号的极端和单调行为以及相关的关键设置参数
Extremal and monotone behaviour of the Sudoku number and related critical set parameters
论文作者
论文摘要
Sudoku编号已定义为各种名称，表明这是一个自然概念。该参数有四个变体，这可能与图形着色问题中关键集的最大和最小大小有关。对于这四个相关参数中的每一个，我们提供了达到最大可能值的图表的一些简单特征。作为主要结果，我们回答了Cooper和Kirkpatrick的一个问题，表明这四个参数中的两个只有两个颜色数量。我们还研究了子图表的单调行为。对于拉丁正方形和sudoku，我们解决了一些变体的超图形着色。
The Sudoku number has been defined under various names, indicating it is a natural concept. There are four variants of this parameter, that can be related to the maximum and minimum size of a critical set in a graph colouring problem. For each of these four related parameters, we present some simple characterizations of the graphs attaining the maximum possible values. As a main result, we answer a question by Cooper and Kirkpatrick, showing that there is monotone behaviour in the number of colours for only two of the four parameters. We investigate the monotone behaviour for the subgraph-order as well. For Latin squares and the Sudoku, we solve some variants for hypergraph colouring.
