On a Generalization of the Ryser‐Brualdi‐Stein Conjecture. Issue 2 (14th April 2014) - Aharoni, Ron; Charbit, Pierre; Howard, David
Abstract A rainbow matching for (not necessarily distinct) sets <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7ksqj" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />F1, …, Fk</alternatives> of hypergraph edges is a matching consisting of k edges, one from each <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7ksp0" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />Fi</alternatives>. The aim of the article is twofold—to put order in the multitude of conjectures that relate to this concept (some first presented here), and to prove partial results on one of the central conjectures.