Partitioning H-free graphs of bounded diameter

A natural way of increasing our understanding NP-complete graph problems is to restrict the input a special class. Classes H-free graphs, that is, graphs do not contain some H as an induced subgraph, have proven be ideal testbed for such complexity study. However, if forbidden contains cycle or claw, then these often stay NP-complete. recent study (MFCS 2019) on k-Colouring problem shows we may still obtain tractable results also bound diameter graph. We continue this line research by initiating impact bounding variety classical vertex partitioning restricted graphs. prove does help Independent Set, but leads new cases closely related 3-Colouring. That show Near-Bipartiteness, Feedback Vertex Odd Cycle Transversal, Acyclic 3-Colouring and Star are all polynomial-time solvable chair-free bounded diameter. To exploit structural property 3-colourable