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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011 Number 2, Pages 54–56 (Mi vmumm674)

This article is cited in 1 paper

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Special embeddings of some disconnected graphs into Euclidean space

K. I. Oblakov, T. A. Oblakova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

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

UDC: 515.162.6

Received: 09.03.2010


 English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2011, 66:2, 90–92

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