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We find the structure of graphs that have no C 4 , $\overline{C}_4$ , C 5 , S 3 , chair and co-chair as induced subgraphs. Then we deduce the structure of the graphs having no induced C 4 , $\overline{C_4}$ , S 3 , chair and co-chair and the structure of the graphs G having no induced C 4 , $\overline{C_4}$ and such that every induced P 4 of G is contained in an induced C 5 of G .

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