Hypergraph Extension Of The Alon-Tarsi List Coloring Theorem

A circulation in a digraph is a spanning subgraph with indegree equal to outdegree at each vertex. Alon and Tarsi proved that a graph is d-choosable when it has an orientation that has no vertex of outdegree at least d and has the property that the numbers of circulations with even-sized and odd-sized edge sets differ. We generalize this to k-uniform hypergraphs for prime k. We use a “hypergraph polynomial“ and a notion of hypergraph orientation defined by choosing a source vertex from each edge.

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Correspondence to Radhika Ramamurthi.

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* Project sponsored by the National Security Agency under Grant Number MDA904-03-1-0037. The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein.

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Ramamurthi, R., West*, D.B. Hypergraph Extension Of The Alon-Tarsi List Coloring Theorem. Combinatorica 25, 355–366 (2005). https://doi.org/10.1007/s00493-005-0020-8

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Mathematics Subject Classification (2000):

  • 05C15
  • 05C65