Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with graph-theory
Search options questions only
not deleted
user 4558
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.
57
votes
4
answers
15k
views
Connectivity of the Erdős–Rényi random graph
It is well-known that if $\omega=\omega(n)$ is any function such that $\omega \to \infty$ as $n \to \infty$, and if $p \ge (\log{n}+\omega) / n$ then the Erdős–Rényi random graph $G(n,p)$ is asymptoti …
- 7,857
27
votes
1
answer
3k
views
Monochromatic triangles in every two-coloring of the plane?
An old problem (possibly due to Erdős and Graham?): given a triangle $T$ and a two-coloring of the plane, does there necessary exist a monochromatic congruent copy of $T$? Here "monochromatic" means …
- 7,857
21
votes
11
answers
4k
views
What are some good examples of non-monotone graph properties?
It seems that many, if not almost all, of the properties studied in graph theory are monotone. (Property means it is invariant under permutation of vertices, and monotone means that the property is e …
- 7,857
20
votes
2
answers
881
views
Is there an analogue of the Erdős–Gallai theorem for simplicial complexes?
The Erdős–Gallai theorem gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.
In particular $d_1 \ge d_2 \ge \dots \ge d_n$ …
- 7,857
18
votes
2
answers
1k
views
In an Erdős–Rényi random graph, what is the threshold for the property "every edge is contai...
Let $G(n,p)$ denote the Erdős–Rényi random graph, where $n$ is the number of nodes and $p$ is the probability for each edge. I'm interested in precisely what range of $p$ the random graph has at least …
- 7,857
14
votes
5
answers
663
views
Do there exist sparse graphs with large crossing number?
Does there exist a sequence of graphs $\{ G_n \}$ such that
$G_n$ has $n$ vertices,
the number of edges of $G_n$ is $O(n)$, and
the crossing number of $G_n$ is $\Omega(n)$?
In particular, do rando …
- 7,857
11
votes
2
answers
3k
views
Algorithm for embedding a graph with metric constraints
Suppose I have a graph $G$ with vertex set $V$, edge set $E \subseteq {V \choose 2}$, a poistive integer $d$, and a weight function $w:E \to \mathbb{R}^{+}$. Is there a nice algorithmic way to decide …
- 7,857
10
votes
1
answer
455
views
For what range of edge probability does the following property hold for random graphs?
Let $G(n,p)$ denote the Erdős–Rényi model of random graph. For a given function $p = p(n)$ we say that $G \in G(n,p)$ asymptotically almost surely has property $\mathcal{P}$ if
$$\mbox{Pr}[G \mbox{ …
- 7,857
10
votes
2
answers
441
views
Higher-dimensional Fáry's theorem?
Fáry's theorem says that every finite simple planar graph admits a planar embedding with straight line edges.
For which $(k,d)$ is it true that every finite $k$-dimensional simplicial complex embeddab …
- 7,857
6
votes
2
answers
724
views
Has the following kind of (minimum degree $d$) random graph been studied?
The following random construction is simple enough that I am guessing it must have been studied. Fix $d \ge 3$, and let $n > d$. For each of the $n$ vertices, pick exactly $d$ other vertices to conne …
- 7,857
4
votes
0
answers
263
views
What are the best bounds to date on the maximum girth of a cubic graph?
The girth of a graph is the length of its smallest cycle. Studying the maximum possible girth for a $k$-regular graph on $n$ vertices is a very well-studied problem.
In the 1988 paper "Ramanujan grap …
- 7,857