Locally Excluding a Minor

A. Dawar, Martin Grohe, S. Kreutzer
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引用次数: 123

Abstract

We introduce the concept of locally excluded minors. Graph classes locally excluding a minor are a common generalisation of the concept of excluded minor classes and of graph classes with bounded local tree-width. We show that first-order model-checking is fixed-parameter tractable on any class of graphs locally excluding a minor. This strictly generalises analogous results by Flum and Grohe on excluded minor classes and Frick and Grohe on classes with bounded local tree-width. As an important consequence of the proof we obtain fixed-parameter algorithms for problems such as dominating or independent set on graph classes excluding a minor, where now the parameter is the size of the dominating set and the excluded minor. We also study graph classes with excluded minors, where the minor may grow slowly with the size of the graphs and show that again, first-order model-checking is fixed-parameter tractable on any such class of graphs.
本地排除未成年人
我们引入了本地排斥未成年人的概念。局部不包含子类的图类是排除子类和局部树宽度有界的图类概念的一般概括。我们证明了一阶模型检验是固定参数可处理的,适用于任何局部不含次要的图类。这严格推广了Flum和Grohe关于排除子类和Frick和Grohe关于局部树宽度有界的类的类似结果。作为证明的一个重要结果,我们得到了图类上不含次要项的支配集或独立集问题的固定参数算法,其中参数是支配集和不含次要项的大小。我们还研究了具有排除次要项的图类,其中次要项可能随着图的大小而缓慢增长,并再次表明,一阶模型检查在任何此类图上都是固定参数可处理的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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