Investigations into the Chen-Raspaud Conjecture for k = 3

TL;DR

This paper reviews multiple approaches to prove the Chen-Raspaud Conjecture for k=3, detailing their methods and failures to guide future research efforts in this area.

Contribution

It provides a comprehensive compilation of attempted proofs and insights into the challenges faced in proving the conjecture for k=3.

Findings

Several approaches failed to prove the conjecture for k=3

Detailed explanations of why each approach failed

Provides a foundation for future research

Abstract

This document collects several approaches attempted in proving the Chen-Raspaud Conjecture for k = 3. Each approach is detailed with full proofs and explanations of why it failed. This compilation aims to provide insights and a foundation for future research on this conjecture.