Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Scheduling Problems and Generalized Graph Coloring
John Machacek  1  
1 : Department of Mathematics [Lansing]  -  Website
Michigan State University East Lansing, MI 48824 USA -  États-Unis

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.

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