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Results tagged with graph-theory
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user 18263
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.
6
votes
0
answers
172
views
Uniformly sampling from the set of all simplicial maps
Let $K$ and $L$ be finite simplicial complexes that remain fixed throughout.
How does one efficiently sample (according to the uniform distribution) elements from the finite set of simplicial map …
- 15.5k
5
votes
3
answers
305
views
Tracking automorphism groups of graph processes
Start with an edgeless graph on $n$ labeled vertices, and note that the automorphism group is $\Sigma_n$, the symmetric group on $n$ elements. Now imagine that we randomly start throwing in all of the …
- 15.5k
4
votes
Accepted
Pairs of paths with the same source and target
Pairs of paths with the same source and target but with no other nodes in common are called parallel paths, at least on the computer science side of things in graph theory -- you can google the term t …
- 15.5k
4
votes
Graph of graph homomorphisms
Warning: the following statement answers an older version of this question.
Let $G$ be the graph you want to realize. Then, $\text{Hom}(\bullet,G) \simeq G$ where $\bullet$ is the graph containing on …
- 15.5k
3
votes
0
answers
57
views
Algorithm to construct metric space endomorphism with controlled square
Given a finite metric space $(M,d)$ with parameters $K \geq 1$ and $\epsilon > 0$, I'd like to algorithmically check for the existence of a non-identity map $\phi:M \to M$ which happens to be $K$-biLi …
- 15.5k
3
votes
Is this graph known?
I think you just have the complement of a line graph here.
Start with $K_n$, the complete directed graph on $n$ vertices (including self-edges). That is, the vertex set is $\lbrace 1,\ldots,n \rbrace …
- 15.5k
2
votes
Recovering a Weighted Graph from Shortest Path Distances
Andreas Blass has produced a simple counterexample to (A) in his answer. I suspect that if your graph is flat in the sense of Andrew Stacey's answer here, then you can in fact recover it from the pair …
- 15.5k
2
votes
2
answers
651
views
Finding a vertex equidistant from two given vertices in a digraph
The question is essentially in the title: while attempting to compute the colimit of a diagram of cell complexes, my colleague and I find ourselves stumped with the following graph theoretic problem:
…
- 15.5k
1
vote
different way of selecting a random graph
There are at least two instances that I can recall where such graphs have been studied. As you've remarked, in general too much depends on the base graph, so you're only going to get somewhere by rest …
- 15.5k
0
votes
Accepted
The terminology for a node's number of in-links in weighted directed graph
The quantity you are asking about is usually called the "fan-in" of node $i$. The dual quantity which counts the number of nodes to which $i$ points is called the "fan-out". The terms are standard at …
- 15.5k