论文标题

删除独立集时,最适合降低色数

When removing an independent set is optimal for reducing the chromatic number

论文作者

Cambie, Stijn, Haslegrave, John, Kang, Ross J.

论文摘要

就图表的最大程度而言,图形的色数必须多大,以确保通过删除顶点减少色数的最有效方法是删除独立的集合?通过将布鲁克斯定理的强大,已知的稳定形式减少,我们可以精确回答这个问题,确定阈值在两个值(实际上是有时是独特的值)之内的足够大最大程度的图表。

How large must the chromatic number of a graph be, in terms of the graph's maximum degree, to ensure that the most efficient way to reduce the chromatic number by removing vertices is to remove an independent set? By a reduction to a powerful, known stability form of Brooks' theorem, we answer this question precisely, determining the threshold to within two values (and indeed sometimes a unique value) for graphs of sufficiently large maximum degree.

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