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SUMMARY:Infinite families of diameter-2 graphs with no triangle or K_2\,t.
  - Sean Eberhard (Warwick)
DTSTART:20260129T143000Z
DTEND:20260129T153000Z
UID:TALK243691@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:David Wood (2023) tried to relax the Moore graph condition by 
 asking whether there are only finitely many diameter-2 graphs with no tria
 ngle 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 H
 offman--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 infinitel
 y many Cayley graphs. This talk is based on joint work with Vladislav Tara
 nchuk and Craig Timmons.
LOCATION:MR12
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