On the Orientation of Graphs and Hypergraphs (2001)
| Citations: | 12 - 4 self |
BibTeX
@MISC{Frank01onthe,
author = {András Frank and Tamás Király and Zoltán Király},
title = {On the Orientation of Graphs and Hypergraphs},
year = {2001}
}
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Abstract
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 S. Khanna, J. Naor and F. B. Shepherd [8], and a new orientation theorem that provides a characterization for (2k+1)-edge-connected graphs.
Citations
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| 9 | Nash-Williams, On orientations, connectivity and odd-vertex-pairings in finite graphs - A - 1960 |
| 7 | On disjoint trees and arborescences, in: Algebraic Methods in Graph Theory - Frank - 1978 |
| 6 | Directed Hypergraphs as a Modelling Paradigm - Gallo, Scutellà - 1998 |
| 4 | Directed network design with orientation constraints - Khanna, Naor, et al. - 2000 |
