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Keyword: chromatic threshold ×Clear all

2 claims from 1 paper

1. Mathematics › Limits and Structures in Graph Theory

   The chromatic thresholds of graphs

   Allen, Böttcher, Griffiths, Kohayakawa and Morris · Advances in Mathematics · 2013

   The paper determines the chromatic threshold of every graph H, showing only three possible values for each chromatic number, and characterises which graphs have which value.

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   1. UncheckedFor any graph H with chromatic number r above 2, its chromatic threshold is one of just three values: (r-3)/(r-2), (2r-5)/(2r-3) or (r-2)/(r-1).“We prove that delta_chi(H) \in {(r-3)/(r-2), (2r-5)/(2r-3), (r-2)/(r-1)} for every graph H with chi(H)=r>2.”
   2. UncheckedThe paper characterises which graphs H have each possible chromatic threshold, so the threshold is determined for every graph H.“We moreover characterise the graphs H with a given chromatic threshold, and thus determine delta_chi(H) for every graph H.”