Minimum size of n-factor-critical graphs and k-extendable graphs

Abstract

We determine the minimum size of $n$-factor-critical graphs and that of $k$-extendable bipartite graphs, by considering Harary graphs and related graphs. Moreover, we determine the minimum size of $k$-extendable non-bipartite graphs for $k=1,2$, and pose a related conjecture for general $k$.

13 pages, 8 figures, published in Graphs and Combinatorics