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, $\alpha \left(H\right)+\omega \left(H\right)\ge |V\left(H\right)|$. (Here $\alpha$ and $\omega$ 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.
doi.org/10.1016/j.dam.2018.12.015
Discrete Applied Mathematics

Litjens, B.M, Polak, S.C, & Sivaraman, V. (2019). Sum-perfect graphs. Discrete Applied Mathematics, 259, 232–239. doi:10.1016/j.dam.2018.12.015