Strong odd coloring in minor-closed classes

TL;DR

This paper proves that in any proper minor-closed graph class, the strong odd chromatic number is bounded by a constant, and it nearly determines this constant for outerplanar graphs.

Contribution

It establishes a universal bound for the strong odd chromatic number in minor-closed classes and nearly identifies this bound for outerplanar graphs.

Findings

Strong odd chromatic number is bounded by a constant in all proper minor-closed classes.

The minimal such constant is almost determined for outerplanar graphs.

Provides new insights into coloring properties of minor-closed graph classes.

Abstract

We show that the strong odd chromatic number on any proper minor-closed graph class is bounded by a constant. We almost determine the smallest such constant for outerplanar graphs.