Alon-Tarsi表着色方法的一种有效实现及其加强
An efficient implementation and a strengthening of Alon-Tarsi list coloring method
摘要：
作为多项式方法在组合学中的第一个应用，Alon和Tarsi给出了一种方法来证明一个图是可选择的（从任何指定大小的列表中可着色）。我们描述了一种有效的方法来实现这种方法，使其可行的测试选择的图形与周围70边。我们还表明，在情况下，阿隆-塔尔西方法未能表明，该图是可选的，图多项式的进一步系数提供限制的列表分配，从该图不能着色。这通常使我们能够从一个给定的列表赋值中确认可着色性，或者通过测试几个列表赋值来决定可选择性。该实现可以在https://gitlab.mff.cuni.cz/dvorz9am/alon-tarsi-method上找到。
英文摘要：
As one of the first applications of the polynomial method in combinatorics, Alon and Tarsi gave a way to prove that a graph is choosable (colorable from any lists of prescribed size). We describe an efficient way to implement this approach, making it feasible to test choosability of graphs with around 70 edges. We also show that in case that Alon-Tarsi method fails to show that the graph is choosable, further coefficients of the graph polynomial provide constraints on the list assignments from which the graph cannot be colored. This often enables us to confirm colorability from a given list assignment, or to decide choosability by testing just a few list assignments. The implementation can be found at https://gitlab.mff.cuni.cz/dvorz9am/alon-tarsi-method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
