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4-cycle-free induced subgraphs of grid graphs
In this paper we consider sets $S$ of vertices of the $n \times n$ grid graph $G_n$ where the induced subgraph $G_S$ having vertex set $S$ contains no $4$-cycles. We first quickly establish the maximum size of any such induced subgraph. Then, for even $n$ we estimate the number of $4$-cycle-free ind
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