Regular factors in vertex-deleted subgraphs of regular graphs
It is proved that for any \(2r\)-regular, \(2r\)-edge-connected graph \(G\) of odd order and any of its vertices \(u\), the graph \(G-u\) has an \(m\)-factor whenever \(1 \leq m \leq r\). This was previously known only for \(m=1\), see \textit{C. H. C. Little, D. D. Grant}, and \textit{D. A. Holton} [On defect-\(d\) matchings in graphs, Discrete Math. 13, 41-54 (1975; Zbl 0304.05120)].
scientific article; zbMATH DE number 626331