Sách Pattern Hypergraphsv

Abstract
The notion of pattern hypergraph provides a unified view of several previously
studied coloring concepts. A pattern hypergraph H is a hypergraph where each
edge is assigned a type Πi that determines which of possible colorings of the edge
are 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 need
not be an interval. We find a simple sufficient and necessary condition on the edge
types Π1, . , Πλ for the existence of a pattern hypergraph H with edges of types
Π1, . , Πλ such that the numbers of colors in proper colorings of H do not form an
interval of integers.