On the monotonicity of games generated by symmetric submodular functions

Authors:
Fedor V. Fomin;Dimitrios M. Thilikos
Affiliations:
Faculty of Mathematics and Mechanics, St. Petersburg State University, Bibliotechnaya sq. 2, St. Petersburg 198904, Russia;Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Campus Nord--Mòdul C5, c/Jordi Girona Salgado 1-3, 08034 Barcelona, Spain
Venue:
Discrete Applied Mathematics - Submodularity
Year:
2003

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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.