Sum-perfect graphs - Litjens, Bart; Polak, Sven; Sivaraman, Vaidy (arXiv.org, 2017)
Inspired by a famous characterization of perfect graphs due to Lovász, we define a graph \(G\) to be sum-perfect if for every induced subgraph \(H\) of \(G\), \(α(H) + ω(H) ≥ |V(H)|\). (Here \(α\) and \(ω\) denote the stability number and clique number, respectively.) We give a set of \(27\) graphs and we prove that a graph \(G\) is sum-perfect if and only if \(G\) does not contain any of the graphs in the set as an induced subgraph.