最大子图问题的复杂性

Proceedings of the tenth annual ACM symposium on Theory of computing Pub Date : 1978-05-01 DOI:10.1145/800133.804356

John M. Lewis

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引用次数: 35

摘要

对于一个固定的图属性，该属性的最大子图识别问题为:给定一个图G和整数k, G是否有一个由k个顶点诱导的满足该属性的子图。本文研究了该问题在不同性质下的复杂性。主要结果是，如果性质是单调性质的任何一类，则极大子图问题是np困难的。这为探究P = ?NP问题提供了一个有希望的方向。

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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On the complexity of the Maximum Subgraph Problem

For a fixed graph property, the Maximum Subgraph Recognition Problem for the property is: Given a graph G and integer k, does G have a subgraph induced by k vertices which satisfies the property. This paper studies the complexity of this problem for various properties. The principal result is that if the property is any one of a wide class of monotone properties, the Maximum Subgraph Problem is NP-hard. This suggests a promising direction of inquiry into the P = ?NP question.

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Proceedings of the tenth annual ACM symposium on Theory of computing

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