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{\bf Mahdad Khatirinejad, Reza Naserasr, Mike Newman, Ben Seamone and Brett Stevens}
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{\bf Digraphs are $2$-Weight Choosable}
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An edge-weighting vertex colouring of a~graph is an edge-weight
assignment such that the accumulated weights at the vertices yield
a~proper vertex colouring. If such an assignment from a~set $S$
exists, we say the graph is $S$-weight colourable.
We consider the $S$-weight colourability of digraphs by defining the
accumulated weight at a vertex to be the sum of the inbound weights
minus the sum of the outbound weights. Bartnicki et al.\ showed that
every digraph is $S$-weight colourable for any set $S$ of size $2$ and
asked whether one could show the same result using an algebraic
approach. Using the Combinatorial Nullstellensatz and a~classical
theorem of Schur, we provide such a~solution.
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