All Questions
Tagged with knot-link topological-graph-theory
3 questions
10
votes
2
answers
598
views
Is there a "simplest" way to embed a graph in 3-space?
I consider embeddings of graphs into 3-space with edges embedded as arbitrary curves. In the simplest (non-trivial) case the graph $G$ is a cycle or union of cycles, in which case the embeddings can ...
10
votes
3
answers
460
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Do triple-linked graphs exist?
Lets say that a finite simple graph $G$ is (intrinsically) fully triple-linked if for each embedding of $G$ into $\Bbb R^3$ we can find three disjoint cycles $C_1,C_2,C_3\subset G$ whose embeddings ...
6
votes
1
answer
142
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Embedding linklessly embeddable graphs without Borromean rings
A linklessly embeddable graph is a graph which can be embedded into $\Bbb R^3$ so that no two of its cycles are linked. For example, the Petersen graph is not such a graph.
Now, I can think of another ...