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Jan 21, 2020 at 8:18 comment added Daniel The "detour number" is what I have been looking for. It even has a connection to treedepth. Thanks to all participants!
Jan 21, 2020 at 8:11 vote accept Daniel
Jan 20, 2020 at 20:59 comment added Hermann Gruber The Wikipedia article on induced paths refers to a quite a bunch of results on graphs with bounded induced path length: en.m.wikipedia.org/wiki/Induced_path
Jan 20, 2020 at 16:09 comment added Gamow There are lots of results on graphs without induced $P_4$ (which are called co-graphs) and on graphs without induced $P_5$; see for instance graphclasses.org/classes/gc_151.html and graphclasses.org/classes/gc_396.html
Jan 20, 2020 at 15:49 comment added Daniel This is a good characterisation! Do you happen to know some if it connected to other graph characteristics or has interesting structural/algorithmical implications?
Jan 20, 2020 at 15:44 vote accept Daniel
Jan 20, 2020 at 15:45
Jan 20, 2020 at 15:44 vote accept Daniel
Jan 20, 2020 at 15:44
Jan 20, 2020 at 13:13 history answered Christian Komusiewicz CC BY-SA 4.0