论文标题
带有Sudoku编号$ N-1 $的图形
Graphs with Sudoku number $n-1$
论文作者
论文摘要
最近，Lau-Jeyaseeli-shiu-arumugam引入了图形“ sudoku颜色”的概念 - 部分$χ（g）$ - $ g $的颜色，这些颜色具有与适当的$χ（g）$ - 所有顶点的颜色的独特扩展。他们介绍了图形的sudoku数量，作为在sudoku着色中的最小彩色顶点。他们猜想连接的图具有sudoku number $ n-1 $，并且只有在完成时才完成。在本说明中，我们证明这是真的。
Recently Lau-Jeyaseeli-Shiu-Arumugam introduced the concept of the "Sudoku colourings" of graphs -- partial $χ(G)$-colourings of $G$ that have a unique extension to a proper $χ(G)$-colouring of all the vertices. They introduced the Sudoku number of a graph as the minimal number of coloured vertices in a Sudoku colouring. They conjectured that a connected graph has Sudoku number $n-1$ if, and only if, it is complete. In this note we prove that this is true.
