Geodesic
Weight choosability of oriented hypergraphs
Ars Mathematica Contemporanea, Tome 16 (2019) no. 1, pp. 111-117.

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The 1-2-3 conjecture states that every simple graph (with no isolated edges) has an edge weigthing by numbers 1, 2, 3 such that the resulting weighted vertex degrees form a proper coloring of the graph. We study a similar problem for oriented hypergraphs. We prove that every oriented hypergraph has an edge weighting satisfying a similar condition, even if the weights are to be chosen from arbitrary lists of size two. The proof is based on the Combinatorial Nullstellensatz and a theorem of Schur for permanents of positive semi-definite matrices. We derive several consequences of the main result for uniform hypergraphs. We also point on possible applications of our results to problems of 1-2-3 type for non-oriented hypergraphs.
DOI : 10.26493/1855-3974.1317.745
Keywords: Oriented hypergraphs, 1-2-3 conjecture, combinatorial nullstellensatz, list weighting 
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Marcin Anholcer; Bartłomiej Bosek; Jarosław Grytczuk. Weight choosability of oriented hypergraphs. Ars Mathematica Contemporanea, Tome 16 (2019) no. 1, pp. 111-117. doi : 10.26493/1855-3974.1317.745. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1317.745/

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