On the orientation of hypergraphs
Ruiz-Vargas, Andres J.
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This is an expository thesis. In this thesis we study out-orientations of hypergraphs, where every hyperarc has one tail vertex. We study hypergraphs that admit out-orientations covering supermodular-type connectivity requirements. For this, we follow a paper of Frank. We also study the Steiner rooted orientation problem. Given a hypergraph and a subset of vertices S ⊆ V, the goal is to give necessary and sufficient conditions for an orientation such that the connectivity between a root vertex and each vertex of S is at least k, for a positive integer k. We follow a paper by Kiraly and Lau, where they prove that every 2k-hyperedge connected hypergraph has such an orientation.