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Results tagged with graph-theory
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user 41873
Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
3
votes
How to find a random cycle in a large graph?
This answer is about directed simple cycles, meaning that the only repeated vertices are the first and last ones.
First, there's no general efficient algorithm to sample uniformly a directed simple cy …
- 1,462
4
votes
0
answers
108
views
Reference on generalization of plane graph duality between bonds and simple cycles
Let $G$ be a plane graph, and $G^*$ its dual. Among the $k$ partitions of the nodes of $G$, I'll call the connected k-partitions those such that each block of nodes of the partition induces a connecte …
- 1,462
3
votes
0
answers
86
views
Reference on the faces of the circulation polytope
On page 4 of Generating all vertices of a polyhedron is hard it is mentioned that the facial structure of the circulation polyhedron* is well understood. I am trying to find a reference for this.
I k …
- 1,462
6
votes
Why do we associate a graph to a ring?
I don't know about the papers you link to specifically, but here is one way to justify introducing graphs into any object you want.
In particular, graphs are useful structures for encoding interaction …
6
votes
3
answers
2k
views
Number of self avoiding paths on a grid graph?
Let $G$ be an $n \times n$ grid graph. Is there anything known about the asymptotic growth rate of the number of self avoiding paths from $(0,0)$ to $(n,b)$ (from the lower left corner to some arbitra …
- 1,462
7
votes
0
answers
170
views
What is known about the distribution of lengths of the cycle you get by adding an edge to a ...
Let $G$ be a finite, connected graph. Let $T$ be a uniform spanning tree, and let $e$ be a uniformly random edge not in $T$. When we add $e$ to $T$, we get a subgraph with a unique cycle, $C$. I am in …
- 1,462