The Independent Set Problem Is FPT for Even-Hole-Free Graphs

Edin Husić, Stéphan Thomassé, Nicolas Trotignon
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引用次数: 2

Abstract

The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem. However, the complexity of computing a maximum independent set (MIS) is a long-standing open question in even-hole-free graphs. From the hardness point of view, MIS is W[1]-hard in the class of graphs without induced 4-cycle (when parameterized by the solution size). Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs. The main idea is to apply twice the well-known technique of augmenting graphs to extend some initial independent set.
偶孔无图的独立集问题是FPT
偶孔无图类与完美图类非常相似,并且确实是导致强完美图定理证明的工具的基石。然而,在无偶孔图中计算最大独立集(MIS)的复杂性是一个长期悬而未决的问题。从硬度上看,MIS在没有诱导4循环的图类中(以溶液大小参数化时)为W[1]-hard。在此基础上,我们证明了当用无偶孔图类的解大小参数化时,MIS是FPT的。其主要思想是应用两次著名的增广图技术来扩展某个初始独立集。
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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