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Results tagged with topological-graph-theory
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user 108884
Graph theoretical questions with a topological flavour. For example, graphs on surfaces, spatial embeddings, and geometric graphs. Use the graph-drawing tag for questions specific to graph drawing (e.g. crossing numbers).
5
votes
0
answers
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When does the ΔY-family of a simple graph contain multigraphs?
Given a graph $G$, its ΔY-family is the smallest family of graphs that contains $G$ and is closed under ΔY- and YΔ-transformations.
Since YΔ-transformations can introduce multi-edges, the ΔY-family of …
- 13.6k
6
votes
1
answer
141
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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 …
- 13.6k
10
votes
2
answers
577
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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 a …
- 13.6k
10
votes
3
answers
435
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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 ar …
- 13.6k