Geodesic
Special embeddings of some disconnected graphs into Euclidean space
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2011), pp. 54-56

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This work considers such embeddings of graphs to $\mathbb{R}3$, that each line contains minimal number of points of the image. It is proved that for every embedding of graph containing disjoined union of two Kuratovski–Pontryagin graphs there exists a line containing four points of the image or more. So disjoint unions of Kuratovski–Pontryagin graphs are minimal $3$-unembedd able graphs. 
@article{VMUMM_2011_2_a8,
     author = {K. I. Oblakov and T. A. Oblakova},
     title = {Special embeddings of some disconnected graphs into {Euclidean} space},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {54--56},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_2_a8/}
}
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K. I. Oblakov; T. A. Oblakova. Special embeddings of some disconnected graphs into Euclidean space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2011), pp. 54-56. http://geodesic.mathdoc.fr/item/VMUMM_2011_2_a8/