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The Haagerup property, which is a strong converse of Kazhdan's property$(T)$, has translations and applications in various fields of mathematics suchas representation theory, harmonic analysis, operator K-theory and so on.Moreover, this group property implies the Baum-Connes conjecture and relatedNovikov conjecture. The Haagerup property is not preserved under arbitrarygroup extensions and amalgamated free products over infinite groups, but it ispreserved under wreath products and amalgamated free products over finitegroups. In this paper, we show that it is also preserved under graph products.We moreover give bounds on the equivariant and non-equivariant$L_p$-compressions of a graph product in terms of the correspondingcompressions of the vertex groups. Finally, we give an upper bound on theasymptotic dimension in terms of the asymptotic dimensions of the vertexgroups. This generalizes a result from Dranishnikov on the asymptotic dimensionof right-angled Coxeter groups.

The Haagerup property is stable under graph products