Counterexamples to a conjecture of Las Vergnas

TL;DR

This paper provides counterexamples to a longstanding conjecture by Las Vergnas from 1988 concerning the properties of the Tutte polynomial in binary matroids, challenging previous assumptions in combinatorics.

Contribution

The authors construct explicit counterexamples that disprove Las Vergnas's conjecture, advancing understanding of Tutte polynomial properties in binary matroids.

Findings

Counterexamples invalidate the conjecture

Disproved assumptions about Tutte polynomial behavior

Enhanced understanding of binary matroid properties

Abstract

We present counterexamples to a 30-year-old conjecture of Las Vergnas [J. Combin. Theory Ser. B, 1988] regarding the Tutte polynomial of binary matroids.