# Refuting conjectures in extremal combinatorics via linear programming

## TL;DR

This paper demonstrates how linear programming techniques and solvers can be effectively used to disprove several longstanding open conjectures in the field of extremal combinatorics.

## Contribution

It introduces a straightforward LP-based approach to refute conjectures, providing a new tool for researchers in extremal combinatorics.

## Key findings

- Successfully refuted multiple open conjectures
- Showed effectiveness of LP methods in combinatorics
- Provided a new approach for disproving conjectures

## Abstract

We apply simple linear programming methods and an LP solver to refute a number of open conjectures in extremal combinatorics.