We show that every cubic graph on n vertices contains a spanning subgraph in which the number of vertices of each degree deviates from n/4 by at most 1/2, up to three exceptions. This resolves the conjecture of Alon and Wei (Irregular subgraphs, Combin. Probab. Comput. 32(2) (2023), 269--283) for cubic graphs.
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Lužar et al. (2024) studied this question.
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