Recognition and probe-partition identification for probe H-free graphs

Determine whether probe H-free graphs can be recognized in polynomial time and whether the distinction between probes and non-probes can be determined for general graphs H.

Background

In the partitioned probe model, the probe and non-probe sets are supplied as part of the input. For most forbidden graphs H, however, the corresponding unpartitioned probe H-free recognition problem and the task of identifying the probes and non-probes are unresolved.

This issue motivates the paper’s focus on partitioned probe H-free graphs, where the partition is known and the complexity of colouring can be studied without first solving the recognition or identification problem.