Open AccessLower Bound of Zero-visibility Cops and Robber Game on the Cube Grid
Author(s) -
Jiahui Wang,
Fang Zhong
Publication year - 2020
Publication title -
computer science and information technology ( cs and it )
Language(s) - English
Resource type - Conference proceedings
DOI - 10.5121/csit.2020.102003
Subject(s) - cube (algebra) , visibility , partition (number theory) , grid , zero (linguistics) , upper and lower bounds , mathematics , combinatorics , computer science , discrete mathematics , geography , geometry , mathematical analysis , linguistics , philosophy , meteorology
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.