# Connectivity of single-element coextensions of a binary matroid

## TL;DR

This paper establishes a precise criterion for when adding a single element to a highly connected binary matroid preserves its connectivity level.

## Contribution

It provides a necessary and sufficient condition for the connectivity of single-element coextensions of an n-connected binary matroid.

## Key findings

- Characterization of connectivity preservation in coextensions
- Necessary and sufficient condition derived
- Applicable to binary matroids with high connectivity

## Abstract

Given an $n$-connected binary matroid, we obtain a necessary and sufficient condition for its single-element coextensions to be $n$-connected.