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In 2012, L\'ev\^eque, Maffray, and Trotignon conjectured that each graph $G$that contains no induced subdivision of $K_4$ is $4$-colorable. In this paper,we prove that this conjecture holds when $G$ contains a $K_{1,2,3}$.

Graphs that contain a $K_{1,2,3}$ and no induced subdivision of $K_4$ are $4$-colorable