Deciding the On-line Chromatic Number of a Graph with Pre-Coloring is PSPACE-Complete

TL;DR

This paper proves that deciding whether the on-line chromatic number of a graph with a given pre-coloring is at most k is a PSPACE-complete problem, highlighting its computational complexity.

Contribution

It establishes the PSPACE-completeness of the on-line chromatic number decision problem with pre-coloring, a previously unresolved complexity classification.

Findings

The problem is PSPACE-complete.

Deciding on-line chromatic number with pre-coloring is computationally hard.

Complexity classification impacts graph coloring algorithms.

Abstract

The problem of determining if the on-line chromatic number of a graph is less than or equal to k, given a pre-coloring, is shown to be PSPACE-complete.