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

TL;DR

This paper characterizes the structure of graphs that exclude specific small induced subgraphs, including cycles of length 4 and 5, their complements, and particular chair-like configurations.

Contribution

It provides a structural description of graphs avoiding certain induced subgraphs, expanding understanding of graph classes defined by forbidden configurations.

Findings

Graphs with no $C_4$, $ar{C}_4$, $C_5$, chair, or co-chair have a specific structural characterization.

The results help classify and analyze graphs based on forbidden induced subgraphs.

The paper advances the theory of graph classes defined by forbidden induced subgraphs.

Abstract

We find the structure of graphs that have no $C_4$, $\overline{C}_4$, $C_5$, chair and co-chair as induced subgraphs.