The structure of graphs with forbidden induced $C_4$, $\overline{C}_4$, $C_5$, $S_3$, chair and co-chair

Abstract

We find the structure of graphs that have no C₄, $\overline{C}_4$, C₅, S₃, chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C₄, $\overline{C_4}$, S₃, chair and co-chair and the structure of the graphs G having no induced C₄, $\overline{C_4}$ and such that every induced P₄ of G is contained in an induced C₅ of G.