On \(\alpha_{r}\gamma_{s}(k)\)-perfect graphs
For \(r\geq 1\), let \(\alpha_r\) and \(\gamma_r\) denote the \(r\)-distance-independence and \(r\)-distance-domination number, respectively. A graph \(G\) is \(\alpha_r\gamma_s(k)\)-perfect if \(\alpha_r(H)- \gamma_s(H)\leq k\) for every induced subgraph \(H\) of \(G\). In 1999, I. Zverovich characterized \(\alpha_1\gamma_1(k)\)-perfect graphs. The present authors characterize claw-free \(\alpha_2\gamma_2(k)\)-perfect graphs and \(\alpha_{2r-1}\gamma_r(k)\)-perfect graphs for \(r\geq 1\).
scientific article; zbMATH DE number 1974995