A new characterization of trivially perfect graphs - Christian Rubio Montiel (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 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.