# Questions tagged [graph-theory]

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.

3,400 questions
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### Bijective operations on finite simple graphs

Let $\mathcal G_n$ be the set of (isomorphism classes of unlabelled) simple graphs on $n$ vertices. I am interested in specific bijective maps $\mathcal G_n\to\mathcal G_n$, defined for all $n$. An ...
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### Strongly rigid regular graphs

A simple, undirected graph $G = (V,E)$ is said to be strongly rigid if the identity is the only graph endomorphism. For which positive integers $k>2$ is there a strongly rigid $k$-regular graph?
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### Maximum chromatic number of a $k$-regular graph [on hold]

Let $c_k$ be the maximum chromatic number that a $k$-regular graph can have. What is $\lim\sup_{k\to\infty}\frac{c_k}{k}$?
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### Description of Linear Time Algorithm for TSP in Halin Graphs

I am looking for a description of the linear time algorithm for the TSP in Halin graphs, that was given in "G. Cornuejols, D. Naddef, and W.R. Pulleyblank. Halin graphs and the travelling ...
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### Colored weighted Graphs with only monochromatic perfect matchings

The following purely graph-theoretic question is motivated by quantum mechanics. Definitions: A bi-colored weighted graph $G(V,E)$ is an undirected graph where every edge is colored, and has a ...
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### Examples of Binary Functions that Yield Regular Graphs with Invertible Adjacency Matrix

Question: What are, provided their existence, examples of functions $f$ with the following properties: \begin{align}f:& \ \mathbb{N}\times\mathbb{N}\ni(i,j)&\mapsto\ \quad\quad\...
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### Applications of De-Bruijn Sequences in “Pure Mathematics”

I know of a few applications of De-Bruijn Sequences and De Bruijn Graphs in combinatorics, applied mathematics, Engineering and computer science. But I have only found one application of De Bruijn ...
Let $G$ be a simple graph. Consider the following edge coloring: We are allowed to use repetitive colors on some edges incident to a vertex such that the result does not contain a sequence of length \$...