Abstract
The paper deals with an extremal problem concerning colorings of hypergraphs with bounded edge degrees. Consider the family of b-simple hypergraphs, in which any two edges do not share more than b common vertices. We prove that for n⩾n0(b), any n-uniform b-simple hypergraph with the maximum edge degree at most c⋅nrn−b is r-colorable, where c>0 is an absolute constant. We also establish some applications of the main result.
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