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 1492
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.
46
votes
8
answers
5k
views
Can a problem be simultaneously polynomial time and undecidable?
The Robertson-Seymour theorem on graph minors leads to some interesting conundrums.
The theorem states that any minor-closed class of graphs can be described by a finite number of excluded minors. As …
- 12.7k
34
votes
1
answer
775
views
Which graphs on $n$ vertices have the largest determinant?
This is a question that seems like it should have been studied before, but for some reason I cannot find much at all about it, and so I am asking for any pointers / references etc.
The determinant of …
- 12.7k
22
votes
0
answers
546
views
Zero curves of Tutte Polynomials?
There is an extensive theory of the real and complex roots of the chromatic polynomial of a graph, a substantial fraction of this being due to the connections between the chromatic polynomial and a pa …
- 12.7k
18
votes
1
answer
1k
views
Bicycles and spanning trees of graphs
A spanning tree in a graph is a connected spanning subgraph with no cycles; it is well known that the number of spanning trees can be found by taking the determinant of a certain matrix related to the …
- 12.7k
15
votes
2
answers
1k
views
What is the smallest uniquely hamiltonian graph with minimum degree at least 3?
I would like to know more about uniquely hamiltonian graphs with minimum vertex degree at least 3, and in particular what is the smallest one.
(Recall that a graph is hamiltonian if it has a cycle pas …
- 12.7k
14
votes
1
answer
759
views
What was Smith's proof of Smith's theorem on Hamilton cycles in cubic graphs?
In a short 1946 paper "On Hamiltonian Circuits", Tutte proved the famous result that an edge in a cubic graph lies in an even number of Hamilton circuits.
He attributed the result to his friend CAB S …
- 12.7k
12
votes
1
answer
2k
views
4-regular graphs with every edge in a triangle
I am interested in regular graphs in which every edge lies in a triangle.
For 3-regular graphs, only the complete graph $K_4$ has this property, so there's not much to see here.
For 4-regular graphs …
- 12.7k
12
votes
0
answers
448
views
Colouring a graph whose edge set is a special union of cliques
I am trying to show that a certain family of graphs can always be properly coloured with at most $6$ colours (where "properly coloured" means that each vertex gets a colour and no edge has both ends t …
- 12.7k
11
votes
1
answer
914
views
Uniquely hamiltonian graphs with minimum degree 4
A graph is uniquely hamiltonian if it has exactly one Hamilton cycle.
As every edge in a cubic graph lies in an even number of Hamilton cycles, a cubic graph cannot be uniquely hamiltonian, and a fa …
- 12.7k
10
votes
2
answers
2k
views
Graphs where every two vertices have odd number of mutual neighbours
There was a rather cute question last week about graphs where every pair of distinct vertices has an odd number of mutual neighbours.
The question was to show that such a graph must have an odd numbe …
- 12.7k
9
votes
0
answers
186
views
Partitioning the vertices of a graph into induced trees
I am looking for previous work regarding graphs whose vertices can be assigned colours (not necessarily a proper colouring) in such a way that each colour class induces a tree.
In particular I am mos …
- 12.7k
9
votes
0
answers
245
views
Heuristic arguments regarding Sheehan's conjecture?
Sheehan conjectured that there are no 4-regular graphs that are uniquely hamiltonian (i.e. have exactly one hamilton cycle).
Evidence that might be loosely seen to be in favour of this conjecture is: …
- 12.7k
9
votes
1
answer
480
views
Has anyone seen this sort of graph property used before?
Consider the following property of a graph $G$:
The graph $G$ has no independent cutset of vertices, $S$, such that the number of components of $G-S$ is more than $|S|$ (the size of $S$).
(That is, …
- 12.7k
8
votes
0
answers
214
views
Has anyone implemented a circle graph recognition algorithm?
A double occurrence word is a circular string of length $2n$ over an alphabet of size $n$ with each letter occurring exactly twice, for example:
ABACCDBD
Given a double occurrence word, we can form …
- 12.7k
8
votes
0
answers
122
views
Is there a non-bipartite hamiltonian cubic graph on $n$ vertices with no $(n-1)$-cycle?
Is there a cubic (3-regular) graph $G$ on $n$ vertices such that:
$G$ is hamiltonian
$G$ has no $(n-1)$-cycles
$G$ is not bipartite
My computer tells me that there are none on up to $24$ vertices …
- 12.7k