Generating All Maximal Induced Subgraphs for Hereditary, Connected-Hereditary and Rooted-Hereditary Properties

TL;DR

This paper studies algorithms for generating all maximal induced subgraphs with specific hereditary properties, providing complexity analyses and reductions to solve the problem efficiently for various properties.

Contribution

It introduces algorithms and complexity analyses for the maximal P-subgraphs problem across hereditary, connected-hereditary, and rooted-hereditary properties, with reduction techniques for restricted cases.

Findings

Algorithms operate in polynomial and incremental polynomial time.

The problem can be solved efficiently for many properties.

Provides complexity class analyses and reduction methods.

Abstract

The problem of computing all maximal induced subgraphs of a graph G that have a graph property P, also called the maximal P-subgraphs problem, is considered. This problem is studied for hereditary, connected-hereditary and rooted-hereditary graph properties. The maximal P-subgraphs problem is reduced to restricted versions of this problem by providing algorithms that solve the general problem, assuming that an algorithm for a restricted version is given. The complexity of the algorithms are analyzed in terms of total polynomial time, incremental polynomial time and the complexity class P-enumerable. The general results presented allow simple proofs that the maximal P-subgraphs problem can be solved efficiently (in terms of the input and output) for many different properties.