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Results tagged with graph-theory
Search options questions only
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user 1737
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.
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Minimal graphs with a prescribed number of spanning trees
As it's long ago since Erdős died and MathOverflow is the second best alternative to him (for discussing personal problems), I'd like to start a fruitful discussion about the following problem that I …
- 8,597
5
votes
1
answer
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Connected graphs that are not 2 connected
In the great book by Harary and Palmer (Graphical Enumeration) one can find many interesting things about graph asymptotics.
For example it is stated that the number of all unlabeled graph is $\sim …
- 1,446
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3
answers
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Laplacian spectrum for product graphs
Let $G$ and $H$ be simple graphs.
I am interested in the Laplacian spectrum for various products of $G$ and $H$ namely the cartesian product, tensor product, lexicographical product and strong product …
- 4,713
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10
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Is the empty graph a tree?
This is a boring, technical question that I stumbled upon while making a contribution to Sage. I would still like to hear a constructive answer so hopefully the question does not get closed.
The que …
- 3,407
3
votes
0
answers
177
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Cubic graphs, unfriendly partitions and hamiltonicity
We say that a $2$-coloring of a graph $G$ is unfriendly if every vertex has at least as many neighbors of the color opposite to his own. Such a coloring always exist and can be obtained by partitionin …
- 2,671
3
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1
answer
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Inertia of the cone graph
Let $\widehat{G}$ be the graph obtained by adding a vertex to a graph $G$ and joining it to all vertices in $V(G)$. Let $\sigma(G)$ be the number of non-positive eigenvalues of the adjacency matrix of …
5
votes
1
answer
307
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A variant of Ramsey numbers
The well known Ramsey number $R(k)$ is the least integer $n$ so that every 2-edge coloring of $K_n$ contains a monochromatic $K_k.$
Another interpretation of the above definition is that every graph …
- 891
19
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3
answers
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A generalization of the triangle counting problem for simple weighted graphs
One nice identity is that $$\operatorname{tr}(A^3)/6$$ counts the number of triangles of a graph with adjacency matrix $A$. It also implies that triangle counting in a graph can be performed in sub-cu …
CommunityBot
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4
answers
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Prime numbers $p$ not of the form $ab + bc + ac$ $(0 < a < b < c )$ (and related questions)
If we ask which natural numbers n are not expressible as $n = ab + bc + ca$ ($0 < a < b < c$) then this is a well known open problem. Numbers not expressible in such form are called Euler's "numeru …
CommunityBot
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Proper edge colorings with no bi-colored 5-paths
Consider you want to properly edge color a graph such that it has no bi-colored cycle. Denote by $\alpha'(G)$ the least number of colors required to color the edges of $G$ in such a way.
It is well k …
- 3,463
8
votes
2
answers
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Isomorphism problem on the class of induced subgraphs of a hypercube
A problem that I am currently studying translates to the problem of deciding whether two induced subgraphs of the hypercube $Q_k$ are isomorphic.
Now it feels to me that this class of graphs is "too …
- 37.7k
4
votes
1
answer
575
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Generating non-isomorphic graphs by adding edges to a given graph
This question is in a way related to the one I posted on math.se. Since the question there did not produce any final answer I am trying my luck here!
I am given a fairly large graph $G$ and subsets $ …
CommunityBot
- 1
7
votes
1
answer
403
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Induced subgraphs of small strongly regular graphs
Consider a strongly regular graph $G$ with parameters $(76,30,8,14).$ Hoffman's bound tells us that $\overline{G}$ has an independent set of size at most $4$ and its not hard to see there are indeed $ …
- 14k
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votes
2
answers
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Minimal graphs of prescribed girth and chromatic number
The well known result of Erdős, states that
Given integers $g > 2$ and $k > 1$ there exist a graph $G$ with $\chi(G) \geq k$ and girth at least $g.$
What I am wondering is
When can we expect …
- 537
4
votes
4
answers
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Determine if a graph has a large clique
This question is quite specific and practical. I hope it is still relevant for MO and will not be removed.
I have a collection $\mathcal{C}$ of graphs having from 5000-6000 vertices and edge density …
CommunityBot
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