On a Generalization of the Ryser‐Brualdi‐Stein Conjecture. Issue 2 (14th April 2014)

• Record Type: Journal Article
• Authors: Aharoni, Ron; Charbit, Pierre; Howard, David
• Is Part Of: Journal of graph theory. Volume 78:Issue 2(2015)
• Page Start: 143
• Page End: 156
• Publication Date: 2014-04-14
• Subjects: Graph theory -- Periodicals; 511
• DOI: 10.1002/jgt.21796
• Languages: English
• ISSNs: 0364-9024

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>A <italic>rainbow matching</italic> for (not necessarily distinct) sets <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7ksqj" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21796:jgt21796-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>F</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>, </mml:mo><mml:mo>…</mml:mo><mml:mo>, </mml:mo><mml:msub><mml:mi>F</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow></mml:math></alternatives></inline-formula> of hypergraph edges is a matching consisting of <italic>k</italic> edges, one from each <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7ksp0" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:03649024:media:jgt21796:jgt21796-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>F</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:math></alternatives></inline-formula>. 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.</p> </abstract>