On the orientation of graphs and hypergraphs
Graph orientation is a well-studied area of combinatorial optimization, one that provides a link between directed and undirected graphs. An important class of questions that arise in this area concerns orientations with connectivity requirements. In this paper we focus on how similar questions can be asked about hypergraphs, and we show that often the answers are also similar: many known graph orientation theorems can be extended to hypergraphs, using the familiar uncrossing techniques. Our results also include a short proof and an extension of a theorem of Khanna et al. (Proceedings of the Eleventh Annual ACMSIAM Symposium on Discrete Alogrithm, 2001, pp. 663671), and a new orientation theorem that provides a characterization for (2k+1)-edge-connected graphs.
orientation connectivity uncrossing directed hypergraph