Perfect $1$-factorizations

Year, pages: 2019, 479 - 496

Let $G$ be a graph with vertex-set $V = V(G)$ and edge-set $E = E(G)$. A $1$-factor of $G$ (also called perfect matching) is a factor of $G$ of degree $1$, that is, a set of pairwise disjoint edges which partitions $V$. A $1$-factorization of $G$ is a partition of its edge-set $E$ into $1$-factors. For a graph $G$ to have a $1$-factor, $\vert V(G) \vert$ must be even, and for a graph $G$ to admit a $1$-factorization, $G$ must be regular of degree $r$, $1 ≤ r ≤ \vert V \vert - 1$.

Rosa, A. 2019. Perfect $1$-factorizations. In Mathematica Slovaca, vol. 69, no.3, pp. 479-496. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0241

Rosa, A. (2019). Perfect $1$-factorizations. Mathematica Slovaca, 69(3), 479-496. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0241