Partial Star Products: A Local Covering Approach for the Recognition of Approximate Cartesian Product Graphs

TL;DR

This paper introduces a local covering method using partial star products to recognize and embed approximate Cartesian product graphs, addressing the challenge of identifying product-like structures in prime graphs.

Contribution

It presents a novel local approach for recognizing approximate Cartesian product graphs through partial star products, enabling global factorization and embedding.

Findings

Effective identification of product-like structures in prime graphs

Successful derivation of global factors from local coverings

Enhanced methods for recognizing approximate Cartesian products

Abstract

This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local approach that covers a graph by small subgraphs, so-called partial star products, and then utilizes this information to derive the global factors and an embedding of the graph under investigation into Cartesian product graphs.