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

Jiahui Wang | Zendy; Farong Zhong | Zendy

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

Author(s) -

Jiahui Wang,

Farong 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.

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