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.
Fomin, F. V., & Thilikos, D. M. (2003). On the monotonicity of games generated by symmetric submodular functions. In Discrete Applied Mathematics (Vol. 131, pp. 323–335). https://doi.org/10.1016/S0166-218X(02)00459-6