An Inductive Proof of Whitney's Broken Circuit Theorem

TL;DR

This paper introduces an inductive proof of Whitney's broken circuit theorem, utilizing the deletion-contraction formula to provide a new perspective on the classical combinatorial result.

Contribution

It offers a novel inductive proof of Whitney's broken circuit theorem, differing from traditional combinatorial proofs.

Findings

New inductive proof established for Whitney's broken circuit theorem

Utilizes deletion-contraction formula in proof methodology

Provides insights into combinatorial structure of broken circuits

Abstract

We present a new proof of Whitney's broken circuit theorem based on induction on the number of edges and the deletion-contraction formula.