Geodesic
The undecidability of joint embedding and joint homomorphism for hereditary graph classes
Discrete mathematics & theoretical computer science, Permutation Patters 2018, Tome 21 (2019) no. 2.

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We prove that the joint embedding property is undecidable for hereditary graph classes, via a reduction from the tiling problem. The proof is then adapted to show the undecidability of the joint homomorphism property as well. 
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     author = {Braunfeld, Samuel},
     title = {The undecidability of joint embedding and joint homomorphism for hereditary graph classes},
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Braunfeld, Samuel. The undecidability of joint embedding and joint homomorphism for hereditary graph classes. Discrete mathematics & theoretical computer science, Permutation Patters 2018, Tome 21 (2019) no. 2. doi : 10.23638/DMTCS-21-2-9. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-21-2-9/

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