Claims

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2025_03_25_chen_ma: Chen and Ma (J. Combin. Theory Ser. B 2026) prove for n at least 600 that K_{n,n+1} is the only graph with 2n + 1 vertices and at least n^2 + n edges without an equal-degree pair joined by a 3-edge path; refereed; partial.

2025_05_01_liu_zeng: A preprint of Liu and Zeng states that for every n at least 2 the graph K_{n,n+1} is the only one with 2n + 1 vertices and at least n^2 + n edges without an equal-degree pair joined by a 3-edge path; unrefereed.

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