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The k-assignment polytope
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6339-2230
2009 (English)Article in journal (Refereed) Published
Abstract [en]

In this paper we Study the structure of the k-assignment polytope, whose vertices are the m x n (0, 1)-matrices with exactly k 1:s and at most one 1 in each row and each column. This is a natural generalisation of the Birkhoff polytope and many of the known properties of the Birkhoff polytope are generalised. A representation of the faces by certain bipartite graphs is given. This tool is used to describe the properties of the polytope, especially a complete description of the cover relation in the face poset of the polytope and an exact expression for the diameter. An ear decomposition of these bipartite graphs is constructed.

Place, publisher, year, edition, pages
2009. Vol. 6, no 2, 148-161 p.
Keyword [en]
Birkhoff polytope, Partial matching, Face poset, Ear decomposition, Assignment polytope
URN: urn:nbn:se:kth:diva-18272DOI: 10.1016/j.disopt.2008.10.003ISI: 000264428900002ScopusID: 2-s2.0-59849107601OAI: diva2:336318
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2010-12-22Bibliographically approved

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Linusson, Svante
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Mathematics (Div.)

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