# A splitter theorem for induced subgraphs

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Maria Chudnovsky, Columbia University
Fine Hall 110

A homogeneous set in a graph $G$ is a subset $X$ of $V(G)$, such that no vertex of $V(G)/X$ has both a neighbor and a non-neighbor in $X$. Let us say that a graph is prime if it has no homogeneous set $X$ with \$1