A note on odd colorings of 1-planar graphs

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an number times on its neighborhood. This notion was recently introduced by Petruševski and Škrekovski, who proved planar admits 9-coloring; they also conjectured 5-coloring. Shortly after, this conjecture confirmed for graphs girth at least seven Cranston; outerplanar Caro, Petruševski, Škrekovski. Building the work Petr Portier then further 8-coloring. In note we prove 1-planar 23-coloring, where it can be drawn in plane so each edge crossed most one other edge.