Degree-balanced decompositions of cubic graphsLužar, Borut (Avtor) Przybyło, Jakub (Avtor) Soták, Roman (Avtor) irregular subgraphrepeated degreesdegree-balanced decompositionWe show that every cubic graph on ▫$n$▫ vertices contains a spanning subgraph, in which the number of vertices of each degree deviates from ▫$\frac{n}{4}$▫ by at most ▫$\frac{1}{2}$▫, up to three exceptions. This resolves the conjecture of Alon and Wei ({\em Irregular subgraphs, Combin. Probab. Comput. 32(2) (2023), 269--283}) for cubic graphs.20252025-05-23 10:22:00Neznano11692sl