Colouring partitioned probe perfect graphs

Prove or disprove that Colouring is solvable in polynomial time on partitioned probe perfect graphs.

Background

Probe chordal graphs are known to be perfect, which yields polynomial-time solvability of Colouring on probe chordal graphs. The paper reports a conjecture by Chandler et al. that the same polynomial-time solvability should hold on the larger class of partitioned probe perfect graphs, but does not resolve it.

References

In 2012, Chandler et al. conjectured that the same holds even for partitioned probe perfect graphs.

— Colouring Probe $H$-Free Graphs  (2505.20784 - Paulusma et al., 27 May 2025) in Section 1, Introduction, subparagraph “Related Work”