A new characterization of trivially perfect graphs - Christian Rubio Montiel (Electronic Journal of Graph Theory and Applications (EJGTA), 2015)
A graph $G$ is trivially perfect if for every induced subgraph the cardinality of the largest set of pairwise nonadjacent vertices (the stability number) $α(G)$ equals the number of (maximal) cliques $m(G)$. We characterize the trivially perfect graphs in terms of vertex-coloring and we extend some definitions to infinite graphs.