Kourovka Problem 21.24 — cograph power graphs are chordal
If the power graph of a finite group contains no induced path on four vertices, must it also contain no induced cycle of length at least four?
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Primary source
Progress summary
A repository records an affirmative answer, but no proof or published verification was found, so the problem is not securely resolved.
The problem asks whether a finite group's power graph being a cograph—having no induced —forces it to be chordal, with no induced cycle of length at least . The available repository entry records the answer as affirmative, but gives neither a proof nor an attribution.
Repository-listed resolution (date unavailable)
The Kourovka repository states that every cograph power graph of a finite group is chordal. This is a claimed resolution, not a verified one: the retrieved literature includes classifications of cograph power graphs and separate chordality results, but the available records do not connect either to a proof of this implication. No counterexample or named solver was found.
Current status (as of August 2026): An affirmative answer is recorded in the Kourovka repository, but no accessible proof or corroborating publication was found; formal verification remains open.
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No solutions have been posted yet.