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On the Monotonicity of Games Generated by Symmetric Submodular Functions

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Graph-Theoretic Concepts in Computer Science (WG 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2204))

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Abstract

Submodular functions have appeared to be a key tool for proving the monotonicity of several graph searching games. In this paper we provide a general game theoretic framework able to unify old and new monotonicity results in a unique min-max theorem. Our theorem, provides a game theoretic analogue to a wide number of graph theoretic parameters such as linear-width and cutwidth.

The work of this author was done in part while he was at the Centro de Modelamiento Matemático, Universidad de Chile and UMR 2071-CNRS, supported by FONDAP and while he was a visiting postdoc at DIMATIA-ITI partially supported by GAČR 201/99/0242 and by the Ministry of Education of the Czech Republic as project LN00A056.

The work of the second author was supported by the EU project ALCOM-FT (IST-99-14186), by the Spanish CYCIT TIC-2000-1970-CE, and by the Ministry of Education and Culture of Spain, Grant number MEC-DGES SB98 0K148809.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Mechanics, St.Petersburg State University, Bibliotechnaya sq.2, St.Petersburg, 198904, Russia

    Fedor V. Fomin

  2. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord - Mòdul C5, c/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Dimitrios M. Thilikos

Authors
  1. Fedor V. Fomin
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  2. Dimitrios M. Thilikos
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rostock, 18051, Rostock, Germany

    Andreas Brandstädt  & Van Bang Le  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Fomin, F.V., Thilikos, D.M. (2001). On the Monotonicity of Games Generated by Symmetric Submodular Functions. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_17

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  • DOI: https://doi.org/10.1007/3-540-45477-2_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42707-0

  • Online ISBN: 978-3-540-45477-9

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