منابع مشابه
Linkless and Flat Embeddings in 3-space in Quadratic Time
We consider embeddings of graphs in the 3-space R (all embeddings inthis paper are assumed to be piecewise linear). An embbeding of a graph in R3 is linkless if every pair of disjoint cycles forms a trivial link (in the senseof knot theory), i.e., each of the two cycles (in R) can be embedded in aclosed topological 2-disk disjoint from the other cycle. Robertson, Seymour and...
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We announce results about flat (linkless) embeddings of graphs in 3space. A piecewise-linear embedding of a graph in 3-space is called flat if every circuit of the graph bounds a disk disjoint from the rest of the graph. We have shown: (i) An embedding is flat if and only if the fundamental group of the complement in 3-space of the embedding of every subgraph is free. (ii) If two flat embedding...
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Robertson, Seymour and Thomas characterized linkless embeddings of graphs by flat embeddings, and determined the obstruction set for linkless embeddings. In this paper, we extend flat embeddings to “primitive embeddings” as linkless embeddings to knotless embeddings. Although the obstruction set for knotless embeddings has not been determined, fundamental theorems and conjectures are obtained.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2012
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-012-9413-9