List Chromatic Number of Finitary Matroids: A Generalization of Seymour's Result

TL;DR

This paper extends Seymour's result by proving that for infinite, loop-free finitary matroids, the chromatic number and list chromatic number are equal, generalizing the finite case to an infinite setting.

Contribution

It generalizes Seymour's theorem from finite to infinite, loop-free finitary matroids, establishing the equality of chromatic and list chromatic numbers in this broader context.

Findings

Chromatic number equals list chromatic number for infinite finitary matroids

Extension of Seymour's finite matroid result to infinite case

Provides a new understanding of coloring properties in infinite matroids

Abstract

Seymour proved that the chromatic numbers and the list chromatic numbers of loop-free finite matroids are the same. In this paper we prove the same statement for infinite, loop-free finitary matroids.