  We define a new type of vertex coloring which generalizes vertex coloring in
graphs, hypergraphs, and simplicial complexes. This coloring also generalizes
oriented coloring, acyclic coloring, and star coloring. There is an associated
symmetric function in noncommuting variables for which we give a
deletion-contraction formula. In the case of graphs this symmetric function in
noncommuting variables agrees with the chromatic symmetric function in
noncommuting variables of Gebhard and Sagan. Our vertex coloring is a special
case of the scheduling problems defined by Breuer and Klivans. We show how the
deletion-contraction law can be applied to scheduling problems. Also, we show
that the chromatic symmetric function determines the degree sequence of uniform
hypertrees, but there exist pairs on $3$-uniform hypertrees which are not
isomorphic yet have the same chromatic symmetric function.
