Special Embeddings of Some Disconnected Graphs into Euclidean Space / Oblakov K.I. and Oblakova T.A. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 2. P. 54-56 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

Embeddings of graphs into R{3} such that each line contains minimal possible number of points of the image are considered. It is proved that for every embedding into R{3} of a graph containing the disjoint union of two Kuratowski-Pontryagin graphs there exists a line containing four points of the image or more. Therefore, disjoint unions of Kuratowski-Pontryagin graphs are minimal 3-nonembeddable graphs.

Key words: graphs, embeddings of graphs, Kuratovski-Pontryagin graphs.

№ 2/2011