Disjoint induced subgraphs of the same order and size
For a graph G, let f(. G) be the largest integer k such that there are two vertex-disjoint subgraphs of G each on k vertices, both inducing the same number of edges. We prove that f(. G). ≥. n/2. -. o(. n) for every graph G on n vertices. This answers a question of Caro and Yuster.
European Journal of Combinatorics
Bollobás, B., Kittipassorn, T., Narayanan, B., & Scott, A. (2015). Disjoint induced subgraphs of the same order and size. European Journal of Combinatorics, 49, 153-166. https://doi.org/10.1016/j.ejc.2015.03.005