A Polynomial Delay Algorithm for Generating Connected Induced Subgraphs of a Given Cardinality

TL;DR

This paper presents a polynomial delay algorithm for efficiently enumerating all connected induced subgraphs of a specified size in a graph, with optimal space complexity.

Contribution

The paper introduces a novel polynomial delay algorithm that enumerates connected induced subgraphs of a given size with improved efficiency and linear space usage.

Findings

Enumerates all connected induced subgraphs of size k in polynomial delay.

Operates with linear space complexity O(n+m).

Provides explicit delay bounds based on graph parameters.

Abstract

We give a polynomial delay algorithm, that for any graph $G$ and positive integer $k$, enumerates all connected induced subgraphs of $G$ of order $k$. Our algorithm enumerates each subgraph in at most $O((k\min\{(n-k),k\Delta\})^2(\Delta+\log k))$ and uses linear space $O(n+m)$, where $n$ and $m$ are respectively the number of vertices and edges of $G$ and $\Delta$ is the maximum degree.