On Covering a Graph Optimally with Induced Subgraphs

TL;DR

This paper investigates the problem of optimally covering a graph with a fixed number of induced subgraphs to minimize the maximum vertices in any subgraph, establishing NP-completeness and providing bounds and algorithms.

Contribution

It proves NP-completeness of the problem, derives lower bounds, and offers approximation algorithms for specific graph classes.

Findings

NP-completeness of the graph covering problem established

Lower bounds on the minimum maximum vertices in subgraphs derived

Approximation algorithms provided for certain graph classes

Abstract

We consider the problem of covering a graph with a given number of induced subgraphs so that the maximum number of vertices in each subgraph is minimized. We prove NP-completeness of the problem, prove lower bounds, and give approximation algorithms for certain graph classes.