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Graph Problems with Obligations

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Book cover Combinatorial Optimization and Applications (COCOA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11346))

Abstract

In this paper we study variants of well-known graph problems: vertex cover, connected vertex cover, dominating set, total dominating set, independent dominating set, spanning tree, connected minimum weighted spanning graph, matching and hamiltonian path. Given a graph \(G=(V,E)\), we add a partition \(\varPi _{V}\) (resp. \(\varPi _{E}\)) of its vertices (resp. of its edges). Now, any solution S containing an element (vertex or edge) of a part of this partition must also contain all the others ones. In other words, elements can only be added set by set, instead of one by one as in the classical situation (corresponding to obligations that are singletons). A motivation is to give a general framework and to study the complexity of combinatorial problems coming from systems where elements are interdependent. We propose hardness and approximation results.

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Authors and Affiliations

  1. LIMOS (UMR CNRS 6158), Université Clermont-Auvergne, Clermont-Ferrand, France

    Alexis Cornet & Christian Laforest

Authors
  1. Alexis Cornet
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  2. Christian Laforest
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Corresponding author

Correspondence to Christian Laforest .

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Editors and Affiliations

  1. Department of Computer Science, Kennesaw State University, Marietta, GA, USA

    Donghyun Kim

  2. Department of Mathematics and Computer Science, North Carolina Central University, Durham, NC, USA

    R. N. Uma

  3. Department of Computer Science, Georgia State University, Atlanta, GA, USA

    Alexander Zelikovsky

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Cornet, A., Laforest, C. (2018). Graph Problems with Obligations. In: Kim, D., Uma, R., Zelikovsky, A. (eds) Combinatorial Optimization and Applications. COCOA 2018. Lecture Notes in Computer Science(), vol 11346. Springer, Cham. https://doi.org/10.1007/978-3-030-04651-4_13

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  • DOI: https://doi.org/10.1007/978-3-030-04651-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04650-7

  • Online ISBN: 978-3-030-04651-4

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