Claims

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1982_06_01_voss: Voss proves that every K4-free graph of chromatic number four has an odd cycle with at least two chords, answering the first question of Problem 1091; refereed in J. Combin. Theory Ser. B and credited by the site's curator.

2026_04_08_alexeev_putterman_sawhney_sellke_valiant: Alexeev, Putterman, Sawhney, Sellke and Valiant give explicit K4-free 4-chromatic graphs whose proper subgraphs are 3-colorable and whose cycles have at most ten chords, so no diagonal count f(r) tending to infinity exists.

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