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Results tagged with graph-theory
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user 11260
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.
2
votes
What is the independence number of hamming graph?
The Hamming graph $H(n,d)$ has $2^n$ vertices labeled by the binary
vectors of length $n$, two vertices being joined by an edge if and
only if the Hamming distance between the corresponding vec …
- 188k
2
votes
Accepted
Solving graph theory problems using neural networks
Here is an example that has found a real-world application, in the context of quantum error correction: The decoding of stabilizer codes is a problem of minimum weight-perfect matching on a graph (for …
- 188k
4
votes
Is there a database/library for the adjacency matrices of notable graphs in the literature?
You could use Sage, which has an extensive collection of graphs built in. Or the graphs known to Mathematica.
- 188k
2
votes
Freely accessible collections of graph data
A very extensive collection of graphs from real world problems is the Stanford Large Network Dataset Collection. The screenshot shows the graphs in the category "social networks", there are a dozen of …
- 188k
8
votes
Accepted
Can the graph removal lemma be proved directly from the triangle removal lemma?
A proof of the Graph Removal Lemma that avoids using the regularity lemma can be found in A new proof of the graph removal lemma (2010). For an explanation why a direct proof of the Graph Removal Lemm …
- 188k
1
vote
Question about graph Ginzburg-Landau equation
If you add an $i$-independent time-dependent term $\delta\theta=\omega t+\gamma$ to $\theta_i$ then the difference $\theta_k-\theta_i$ that appears in the amplitude equation is unchanged. The phase e …
- 188k
10
votes
regular graphs with the smallest eigenvalue -2?
Connected regular graphs with smallest eigenvalue at least $−2$ are either a line graph, a cocktail party graph, or the number of vertices is at most 28.
P. J. Cameron, J. M. Goethals, J. J. Seidel a …
- 188k
11
votes
Accepted
Intuition of the energy of a graph
The name "energy" only makes physical sense for a bipartite graph, where the eigenvalues of the adjacency matrix come in pairs $\pm\lambda$. If graph represents a molecule, the adjacency matrix is the …
- 188k
2
votes
Concentration of measure in graph theory
Sharp concentration of the chromatic number on random graphs, Eli Shamir and Joel Spencer (1987).
The concentration of measure phenomenon is used to prove concentration of the chromatic number for ra …
- 188k
2
votes
Accepted
Is there a monograph or review of Hamiltonian cycles of graphs (or long cycles of graphs)？
Q: Is there a monograph (or review) of Hamiltonian cycles of graphs (or long cycles of graphs)？
One possible answer (from a specific perspective) is
Hamiltonian Cycle Problem and Markov Chains (2012)
…
- 188k
3
votes
About a result by P. Erdős and H. Sachs on graph with large girth
I OCR'd the text from the abstract (the pdf contains poor quality text, OCR'ing it yourself gives better results), pasted the OCR'ed text into DeepL, and received the following, without any edits from …
- 188k
3
votes
Accepted
A reference for Wagner's Theorem
A text book reference is Graph Decompositions: A Study in Infinite Graph Theory by Reinhard Diestel (1990), see chapter 6.
- 188k
5
votes
When is MAXCUT "easy"?
On the complexity of the maximum cut problem (2005)
The complexity of the SIMPLE MAXCUT problem (MAX CUT with all edge weights equal to unity) is investigated for
several special classes of grap …
- 188k
10
votes
How to effectively search Internet for graphs not for function graphs?
Use Google Scholar instead of plain Google; I simply entered graphs and pretty much all the items returned by Google Scholar refer to graphs in the mathematical context.
It also suggests helpful speci …
- 188k
1
vote
Accepted
Good graph theory and combinatorics book
Combinatorics and Graph Theory
This book covers a wide variety of topics in combinatorics and graph
theory. It includes results and problems that cross subdisciplines,
emphasizing relationship …
- 188k