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Variations of the cop and robber game on graphs
[article]

2017
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arXiv
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pre-print

We prove new theoretical results about several variations of the cop and robber game on graphs. First, we consider a variation of the cop and robber game which is more symmetric called the cop and killer game. We prove for all $c < 1$ that almost all random graphs are stalemate for the cop and killer game, where each edge occurs with probability $p$ such that $\frac{1}{n^{c}} \le p \le 1-\frac{1}{n^{c}}$. We prove that a graph can be killer-win if and only if it has exactly $k\ge 3$ triangles

arXiv:1710.11352v1
fatcat:3hwzj5mdlzbxfcsslzh76v7bde