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.

Keywords

• forbidden subgraph, threshold graph, $c_4$, $p_4$