Recognition of probe H-free graphs and identification of probes

Develop polynomial-time recognition algorithms for probe H-free graphs and determine the distinction between probes and non-probes for general graphs H.

Background

In the probe graph model, the input graph is accompanied by a partition into probes and non-probes, with only edges involving probes known explicitly. Although recognition is possible for some forbidden graphs such as P_4, the paper states that recognition and identification of the probe/non-probe partition remain unresolved for most graphs H. Consequently, the paper generally studies partitioned probe H-free graphs, where the partition is supplied as part of the input.