On the complexity of the Maximum Subgraph Problem

Abstract

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.