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Infinite families of diameter-2 graphs with no triangle or K_2,t.

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  • UserSean Eberhard (Warwick)
  • ClockThursday 29 January 2026, 14:30-15:30
  • HouseMR12.

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David Wood (2023) tried to relax the Moore graph condition by asking whether there are only finitely many diameter-2 graphs with no triangle or K_2, t for any fixed t apart from stars. Let W_t be the class of such graphs. For t = 2 these are the Moore graphs of diameter 2, so the Hoffman—Singleton Theorem implies that W_2 is finite. In this talk I will show a construction of infinitely many W_3 graphs. I will also show that W_5 contains infinitely many regular graphs and that W_7 contains infinitely many Cayley graphs. This talk is based on joint work with Vladislav Taranchuk and Craig Timmons.

This talk is part of the Combinatorics Seminar series.

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