List total coloring of pseudo-outerplanar graphs

TL;DR

This paper proves that pseudo-outerplanar graphs with maximum degree at least 5 can be list colored with at most +1 colors, extending total coloring results to this class.

Contribution

It establishes the total (+1)-choosability of pseudo-outerplanar graphs for  5, a new result in graph coloring theory.

Findings

Pseudo-outerplanar graphs are +1 total -choosable for   5.

The result extends total coloring bounds to a broader class of graphs.

Provides new insights into coloring properties of pseudo-outerplanar graphs.

Abstract

A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. It is proved that every pseudo-outerplanar graph with maximum degree \Delta\geq 5 is totally (\Delta+1)-choosable.