A characterization of a graph which has a 2-factor
For a graph \(G\) let FBUB\((G)\) be the sum of the number of vertices of odd degree and twice the number of isolated vertices in \(G\). Set \( \text{BUB}(G) = \min\{ \text{FBUB}(G') : G' \text{ spanning subgraph of } G\}\). The author proves that a graph \(G\) has a 2-factor if and only if BUB\((G-S) \leq 2|S|\) for every proper subset \(S\) of the vertex set of \(G\).
scientific article; zbMATH DE number 1528566