All buildable graphs H (those whose prime induced subgraphs have a degree-1 vertex) satisfy the Erdős-Hajnal conjecture when paired with a buildable complement, with infinitely many such primes, proved by iterative sparsification.
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Induced subgraph density. IV. New graphs with the Erd\H{o}s-Hajnal property
All buildable graphs H (those whose prime induced subgraphs have a degree-1 vertex) satisfy the Erdős-Hajnal conjecture when paired with a buildable complement, with infinitely many such primes, proved by iterative sparsification.