A Bound on the Shannon Capacity via a Linear Programming Variation

TL;DR

This paper introduces a new linear programming-based upper bound on the Shannon capacity of graphs, which can outperform existing bounds like Lovász theta and Haemers minimum rank, and also provides a new bound on Index Coding broadcast rate.

Contribution

The paper presents a novel linear programming variation that improves upper bounds on Shannon capacity and Index Coding broadcast rate over previous methods.

Findings

Our bound outperforms Lovász theta and Haemers bounds.

The new bound provides tighter estimates for Shannon capacity.

A new upper bound on Index Coding broadcast rate is established.

Abstract

We prove an upper bound on the Shannon capacity of a graph via a linear programming variation. We show that our bound can outperform both the Lov\'asz theta number and the Haemers minimum rank bound. As a by-product, we also obtain a new upper bound on the broadcast rate of Index Coding.