In this paper, we give two new criteria of detecting the checkerboard colorability of virtual links by using the odd writhe and the arrow polynomial of virtual links, respectively. As a result, we prove that 6 virtual knots are not checkerboard colorable, leaving only one virtual knot whose checkerboard colorability is unknown among all virtual knots up to four classical crossings.

中文翻译：

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关于棋盘可着色虚拟链接的箭头多项式

在本文中，我们分别使用奇数旋转和虚拟链接的箭头多项式给出了两个新的检测虚拟链接棋盘可着色性的标准。结果，我们证明了 6 个虚拟结不是棋盘可着色的，在最多四个经典交叉的所有虚拟结中，仅留下一个其棋盘可着色性未知的虚拟结。