Can I read The one-visibility Localization game on EtoBox?

The one-visibility Localization game by Bonato, Anthony; Marbach, Trent G.; Molnar, Michael; Nir, JD is a scholarly article available to read on EtoBox.

What is The one-visibility Localization game about?

We introduce a variant of the Localization game in which the cops only have visibility one, along with the corresponding optimization parameter, the one-visibility localization number $\zeta_1$. By developing lower bounds using isoperimetric inequalities, we give upper and lower bounds for $\zeta_1$ on $k$-ary trees with $k\ge 2$ that differ by a multiplicative constant, showing that the parameter is unbounded on $k$-ary trees. We provide a $O(\sqrt{n})$ bound for $K_h$-minor free graphs of order $n$, and we show Cartesian grids meet this bound by determining their one-visibility localization number up to four values. We present upper bounds on $\zeta_1$ using pathwidth and the domination number and give upper bounds on trees via their depth and order. We conclude with open problems.

Author

Bonato, Anthony; Marbach, Trent G.; Molnar, Michael; Nir, JD

Published

2023

Language

EN