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. © 2003 Elsevier B.V. All rights reserved.
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