We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and
simplicial complexes. To this coloring there is an associated symmetric function in noncommuting variables for which
we give a deletion-contraction formula. In the case of graphs our 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.