Equitable orientations of sparse uniform hypergraphs

Nathann Cohen (1, 2, 3) , William Lochet (3, 4, 5, 6)

1 CNRS - Centre National de la Recherche Scientifique
2 LRI - Laboratoire de Recherche en Informatique
3 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
4 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
5 I3S - Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis
6 MC2 - Modèles de calcul, Complexité, Combinatoire

Caro, West, and Yuster studied how r-uniform hypergraphs can be oriented in such a way that (generalizations of) indegree and outdegree are as close to each other as can be hoped. They conjectured an existence result of such orientations for sparse hypergraphs, of which we present a proof.

Domaines: Combinatoire [math.CO]; Algorithme et structure de données [cs.DS]; Complexité [cs.CC]

Nathann Cohen, William Lochet. Equitable orientations of sparse uniform hypergraphs. The Electronic Journal of Combinatorics, 2016, 23 (4), pp.4-31. ⟨hal-01417832⟩