All Questions
Tagged with topological-graph-theory reference-request
9 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 ...
- 687
1
vote
0
answers
109
views
What is known about this generalization of planar dual?
So it is well known that given a planar graph, $G$, embedded in the plane (without edge crossing, so a planar embedding). One can construct the planar dual, $G^*$. What is perhaps slightly less well-...
- 461
2
votes
1
answer
111
views
Maximum genus of an abstract "cycle complex"
Let us define an abstract "cycle complex" as the following combinatorial object: it is $(V, C)$, where $V$ is a set of $n$ nodes, $C$ is a set of $c$ cyclically ordered subsets of $V$, each ...
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- 1
2
votes
0
answers
28
views
(Cyclic) edge-connectivity for lifts of voltage graphs?
Can someone point me in the direction of what's known about edge connectivity (or, ideally, cyclic edge connectivity) of graphs which are lifts of voltage graphs? It seems like someone should have ...
4
votes
1
answer
539
views
Connection between connectivity and cohesion of a graph
Tutte [1] proved that, for every $3$-connected graph $G$ and vertices $u$ and $v$, there exists a nonseparating $uv$-path.
A graph $G$ is $t$-cohesive if $G$ is connected, has at least two vertices, ...
5
votes
2
answers
373
views
Genus of Tutte-Coxeter Graph
What is the genus of the Tutte-Coxeter graph -- the incidence graph of the
GQ of order 2? Seems like it should be well known, since nearly every other
parameter for that graph is known, but I can ...
- 5,259
2
votes
0
answers
215
views
Polyhedral embeddings of large face-width where all faces have the same length
Where can I find examples of polyhedral embeddings of simple graph with large face-width, such that all the faces have the same length?
By polyhedral embedding I mean an embedding of the graph on a ...
- 884
3
votes
0
answers
219
views
Double duality for "geometrically defined" graph imbeddings
I am studying imbeddings of (connected, undirected, unweighted, multi-)graphs on oriented surfaces of arbitrary genus, and I am searching for a reference for the statement that the dual of the dual ...
- 2,830
13
votes
1
answer
718
views
Homotopy theory for spanning trees of a graph
I am studying a paper of L. Lovász, ``A homology theory for spanning trees of a graph,'' but professor Babai has told me that Lovász later realized that this work is better framed in the language of ...
- 8,803