Geodesic
Introduction to the "prisoners and guards" game
Journal of integer sequences, Tome 12 (2009) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the half-dependent problem for the king graph $K_{n}$. We give proofs to establish the values $h(K_{n})$ for $n \in {1,2,3,4,5,6}$ and an upper bound for $h(K_{n})$ in general. These proofs are independent of computer assisted results. Also, we introduce a two-player game whose winning strategy is tightly related with the values $h(K_{n})$. This strategy is analyzed here for $n = 3$ and some facts are given for the case $n = 4$. Although the rules of the game are very simple, the winning strategy is highly complex even for $n = 4$.
Classification : 05D99, 91A05, 91A24
Keywords: upper bounds, winning strategies, maximal configurations, domination in graphs 
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Howard, Timothy; Ionascu, Eugen J.; Woolbright, David. Introduction to the "prisoners and guards" game. Journal of integer sequences, Tome 12 (2009) no. 1. http://geodesic.mathdoc.fr/item/JIS_2009__12_1_a2/