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We prove that, for integers n/>2 and k~>2, every tree with n vertices contains an induced subgraph of order at least 2/(n + 2k-3)/(2k-1)j with all degrees congruent to 1 mod-ulo k. This extends a result of Radcliffe and Scott, and answers a question of Caro et al.

- David M Berman, A J Radcliffe, A D Scott, Hong Wang, Larry Wargo

We prove that, for integers n ≥ 2 and k ≥ 2, every tree with n vertices contains an induced subgraph of order at least 2(n + 2k − 3)/(2k − 1) with all degrees congruent to 1 modulo k. This extends a result of Radcliffe and Scott, and answers a question of Caro, Krasikov and Roditty.

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