Color-Critical Graphs and Hypergraphs with Few Edges : A Survey A

@inproceedings{Kostochka2011ColorCriticalGA,
  title={Color-Critical Graphs and Hypergraphs with Few Edges : A Survey A},
  author={Alexandr V. Kostochka},
  year={2011}
}
A hypergraph is color-critical if deleting any edge or vertex reduces the chromatic number; a color-critical hypergraph with chromatic number k is k-critical. Every k-chromatic hypergraph contains a k-critical hypergraph, so one can study chromatic number by studying the structure of k-critical (hyper)graphs. There is vast literature on k-critical graphs and hypergraphs. Many references can be found in [23, Chapters 5 and 1]. 

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