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For a finite graph Γ, let G(Γ) be the right-angled Artin group defined by the complement graph of Γ. We show that, for any linear forest Λ and any finite graph Γ, G(Λ) can be embedded into G(Γ) if and only if Λ can be realized as a full subgraph of Γ. We also prove that if we drop the assumption that Λ is a linear forest, then the above assertion does not hold, namely, for any finite graph Λ, which is not a linear forest, there exists a finite graph Γ such that G(Λ) can be embedded into G(Γ), though Λ cannot be embedded into Γ as a full subgraph.

Right-angled Artin groups and full subgraphs of graphs