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Path Partitions, Cycle Covers and Integer Decomposition

(Lecture Note)

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Book cover Graph Theory, Computational Intelligence and Thought

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5420))

Abstract

A polyhedron P has the integer decomposition property, if every integer vector in kP is the sum of k integer vectors in P. We explain that the projections of polyhedra defined by totally unimodular constraint matrices have the integer decomposition property, in order to deduce the same property for coflow polyhedra defined by Cameron and Edmonds. We then apply this result to the convex hull of particular stable sets in graphs. Therebye we prove a generalization of Greene and Kleitman’s well-known theorem on posets to arbitrary digraphs which implies recent and classical purely graph theoretical results on cycle covers, is closely related to conjectures of Berge and Linial on path partitions, and implies these for some particular values of the parameters.

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Author information

Authors and Affiliations

  1. Laboratoire G-SCOP, CNRS, 46, Avenue Félix Viallet, 38000 Grenoble, 38031, Grenoble, Cedex 1, France

    András Sebő

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  1. András Sebő
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Editor information

Editors and Affiliations

  1. The Caesarea Rothschild Institute, Mount Carmel, University of Haifa, 31905, Haifa, Israel

    Marina Lipshteyn

  2. Department of Computer Science and Mathematics, Ariel University Center of Samaria, 40700, Ariel, Israel

    Vadim E. Levit

  3. Department of Computer Science, Colorado State University, 80523-1873, Fort Collins, CO, USA

    Ross M. McConnell

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Sebő, A. (2009). Path Partitions, Cycle Covers and Integer Decomposition. In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds) Graph Theory, Computational Intelligence and Thought. Lecture Notes in Computer Science, vol 5420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02029-2_18

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  • DOI: https://doi.org/10.1007/978-3-642-02029-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02028-5

  • Online ISBN: 978-3-642-02029-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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