Mrs. Correct and Majority Colorings

TL;DR

This paper simplifies proof techniques and extends results on majority colorings of directed graphs, including an online variant called paintability, providing a unified approach to these coloring problems.

Contribution

It introduces a simplified, unified method for analyzing majority colorings and their generalizations, including the online paintability variant.

Findings

Simplified proof techniques for majority coloring.

Generalization of results to paintability (online list coloring).

Unified approach applicable to various coloring extensions.

Abstract

A majority coloring of a directed graph is a vertex coloring in which each vertex has the same color as at most half of its out-neighbors. In this note we simplify some proof techniques and generalize previously known results on various generalizations of majority coloring. In particular, our unified and simplified approach works for paintability - an on-line analog of the list coloring.