The Erdős-Hajnal Property for the six-vertex Graph with Edge Set $\{ab,bc,cd,de,af,bf,df\}$

We prove that the six-vertex graph with edge set $\{ab,bc,cd,de,af,bf,df\}$ has the Erdős-Hajnal property. The proof adapts the iterative-sparsification method of Nguyen, Scott, and Seymour within the comb-based framework of Huang, Ju, and Zhou.