Compression with wildcards: Enumerating specific induced subgraphs, and packing them as well

TL;DR

This paper introduces algorithms for enumerating specific induced subgraphs and their packings in a graph, focusing on connected sets and various graph types, with applications in graph analysis.

Contribution

It presents novel algorithms for enumerating connected induced subgraphs and packings of such subgraphs for different graph types, expanding on existing enumeration methods.

Findings

Algorithms efficiently enumerate connected induced subgraphs.

Methods handle various graph types beyond simple connectivity.

Enumeration techniques are applicable to complex graph analysis tasks.

Abstract

Various algorithms have been proposed to enumerate all connected induced subgraphs of a graph $G=(V,E)$. As a variation we enumerate all "packings of connected sets", i.e. partitions $\Pi$ of $V$ with the property that each part of $\Pi$ induces a connected subgraph. More generally, for various types $T$ of graphs we do (one or both of) the following: (i) enumerate all type $T$ (induced) subgraphs of a given graph $G$, or (ii) enumerate all packings of type $T$ subgraphs of $G$