# Proof of the List Coloring Conjecture for line perfect multigraphs

## TL;DR

This paper proves that for line perfect multigraphs, the chromatic index equals the list chromatic index, extending Galvin's bipartite multigraph result, with acknowledgment of prior similar work by Peterson and Woodall.

## Contribution

It establishes the equality of chromatic index and list chromatic index for line perfect multigraphs, generalizing existing results to a broader class of graphs.

## Key findings

- Chromatic index equals list chromatic index for line perfect multigraphs
- Extension of Galvin's bipartite multigraph result
- Acknowledgment of prior similar work by Peterson and Woodall

## Abstract

We prove that for a line perfect multigraph the chromatic index is equal to the list chromatic index. This is a generalization of Galvin's result on bipartite multigraphs. Soon after the first version was submitted to arxiv, I found out that the same result has already been achieved in an older paper by Peterson and Woodall, by a similar but not entirely the same method.