Entropy-Based Proofs of Combinatorial Results on Bipartite Graphs

TL;DR

This paper introduces entropy-based proofs for various combinatorial bounds in bipartite graphs, providing new insights and refined results using Shannon entropy properties.

Contribution

It presents novel entropy-based proof techniques for known and refined bounds in bipartite graph combinatorics, expanding methodological tools.

Findings

Upper bounds on independent sets in bipartite graphs

Lower bounds on minimal colors in constrained edge coloring

Lower bounds on the number of walks of given length

Abstract

This work considers new entropy-based proofs of some known, or otherwise refined, combinatorial bounds for bipartite graphs. These include upper bounds on the number of the independent sets, lower bounds on the minimal number of colors in constrained edge coloring, and lower bounds on the number of walks of a given length in bipartite graphs. The proofs of these combinatorial results rely on basic properties of the Shannon entropy.