Lower Bound of Zero-visibility Cops and Robber Game on the Cube Grid

Abstract

Zero-visibility cops and robber game is a variant of the classical model. The robber is invisible in the zero-visibility game. In this paper, we study the zero-visibility cops and robber game on the cube grid. We first study a partition problem of the cube grid. Then we prove the lower bound on the zero-visibility cop number of the cube grid by using the results in the partition. We also show the lower bound is a quadratic polynomial about n.