AbstractThe notion of pattern hypergraph provides a unified view of several previouslystudied coloring concepts. A pattern hypergraph H is a hypergraph where eachedge is assigned a type Πi that determines which of possible colorings of the edgeare proper. A vertex coloring of H is proper if it is proper for every edge. In general,the set of integers k such that H can be properly colored with exactly k colors neednot be an interval. We find a simple sufficient and necessary condition on the edgetypes Π1, . , Πλ for the existence of a pattern hypergraph H with edges of typesΠ1, . , Πλ such that the numbers of colors in proper colorings of H do not form aninterval of integers...