Odd coloring of two subclasses of planar graphs

Abstract

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an odd number of times on its neighborhood. Petruševski and Škrekovski conjectured in 2021 that every planar graph admits an odd 5-coloring. We confirm this conjecture for outer-1-planar graphs and 2-boundary planar graphs, which are two subclasses of planar graphs.