The asymptotic number of graphs not containing a fixed color-critical subgraph

@article{Prmel1992TheAN,
  title={The asymptotic number of graphs not containing a fixed color-critical subgraph},
  author={Hans J{\"u}rgen Pr{\"o}mel and Angelika Steger},
  journal={Combinatorica},
  year={1992},
  volume={12},
  pages={463-473}
}
For a finite graph G let Forb(H) denote the class of all finite graphs which do not contain H as a (weak) subgraph. In this paper we characterize the class of those graphs H which have the property that almost all graphs in Forb(H) are t-colorable. We show that this class corresponds exactly to the class of graphs whose extremal graph is the Turs Tn(l). An earlier result of Simonovits (Extremal graph problems with symmetrical extremal graphs. Additional chromatic conditions, Discrete Math. 7… CONTINUE READING

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