I'm interested in hypergraphs for which there are known (nontrivial) lower bounds on the chromatic number. If someone could point me to existing literature (survey papers etc) on this topic that would be great.
2026-03-25 15:45:40.1774453540
Hypergraph Colorability
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I am not aware of any good overview references for hypergraph colouring. However, Voloshin wrote a nice book on colouring mixed hypergraphs, which generalize the usual colouring condition.
In addition to requiring that at least two vertices in every edge receive Different colours (as in the usual setup), in a mixed hypergraph some edges may be required to have at least two vertices that both receive a Common colour. One can just assume that there are no Common restrictions, so this is a generalization.
There are then several nice classes of mixed hypergraphs for which one can give non-trivial bounds on the chromatic number. These include pseudo-chordal and $C$-perfect mixed hypergraphs. Voloshin also provides over two hundred references, many of them relating to the classical setting.