\((2,k)\)-factor-critical graphs and toughness
A graph \(G\) is \((r,k)\)-factor-critical if \(G-W\) has an \(r\)-factor for every \(W\subseteq V(G)\) with \(|W|= k\). It is shown that every \(\tau\)-tough graph of order \(n\) with \(\tau\geq 2\) is \((2,k)\)-factor-critical for every nonnegative integer \(k\leq \min\{2\tau-2, n- 3\}\). This settles a conjecture of Liu and Yu.
scientific article; zbMATH DE number 1332847