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Fourientations and the Tutte polynomial
2017
Research in the Mathematical Sciences
A fourientation of a graph is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. Fixing a total order on the edges and a reference orientation of the graph, we investigate properties of cuts and cycles in fourientations which give trivariate generating functions that are generalized Tutte polynomial evaluations of the form We introduce an intersection lattice of 64 cut-cycle fourientation classes enumerated by generalized
doi:10.1186/s40687-017-0107-z
fatcat:kukntojwjzhtbpg3pozjior3x4