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For a graph $G$, let $f(G)$ be the largest integer $k$ for which there existtwo vertex-disjoint induced subgraphs of $G$ each on $k$ vertices, bothinducing the same number of edges. We prove that $f(G) \ge n/2 - o(n)$ forevery graph $G$ on $n$ vertices. This answers a question of Caro and Yuster.

Disjoint induced subgraphs of the same order and size