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Results tagged with graph-theory
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user 31310
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.
0
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Cycle-Sculpturing with Minimal Vertex-Deletion
given a simple, finite and symmetric graph $G(V,E)$ with $n$ vertices and at least $n$ edges
Question:
how can the smallest set of vertices $W\subset V$ be calculated for which the graph induced by $ …
- 13.2k
1
vote
1
answer
54
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Complexity of maximum weight-sum matching for cycle graphs
I need to determine a matching with maximal weight-sum for a cycle graph with positive, negative and zero edge-weights.
Question:
What is the fastest way of calculating such a matching?
Because of t …
- 13.2k
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0
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23
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Building hypercubes from the bottom up
let $H^k$ denote a $k$-dimensional hypercube in a complete symmetric graph $G(V,E)$ without self-loops and parallel edges; let $|V|=2^n$ be the number of vertices.
setting
$\mathbb{H}^0 := V$, i.e. th …
- 13.2k
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1
answer
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Name for generalization of trees to digraphs
One definition of tree in graph theory could be as follows:
A tree is a(n undirected) graph for which there is a unique (undirected) path between any pair of vertices.
This suggest a possible defini …
- 13.2k
0
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32
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Enumeration of flat integral $K_4$
Question:
What is known about the enumeration of all $(a,b,c,d,e,f)\in\mathbb{N}^6_+: \\ \quad\operatorname{GCD}(a,b,c,d,e,f)=1\ \\ \land\ \exists \lbrace x_1,x_2,x_3,x_4\rbrace\subset\mathbb{E}^2:\ …
- 13.2k
2
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2
answers
202
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Isometric embeddings of metric $K_{n+1}$ in $\mathbb{R}^n$
Question:
is it always possible to embed a complete, symmetric and metric graph $G$ with $n+1$ vertices isometrically in $\mathbb{R}^n$?
I'm convinced it must be true, but can't remember having seen …
- 13.2k
2
votes
1
answer
124
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Constructing optimal Hamilton cycles from optimal Hamilton paths
Question:
can the shortest Hamilton cycle in a complete symmetric graph with weighted edges be constructed from the shortest Hamilton path in the same graph by connecting its ends and then exchanging …
- 13.2k
0
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0
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89
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Relation of minimum spanning trees to the shortest Hamiltonian path problem
Spanning trees can be decomposed into a minimal set of maximal path graphs, whose vertices have degree two exactly if they also have degree two in the spanning tree; lets call these paths tree paths.
…
- 13.2k
2
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2
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Existence of certain regular graphs
Question:
what can be said about the existence of $2k$ regular graphs, $1\lt k$ that have a $1$-factor and a $2$-factor?
Provided their existence, what is/are the smallest for $k$?
The graphs must b …
- 13.2k
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1
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Algorithmic complexity of calculating maximum weight $k$-regular subgraphs
Question:
what is known about the complexity of calculating the heaviest $k$-regular subgraph of a weighted symmetric graph if edge-weights can also be negative?
Please note that in contrast to $k$- …
- 13.2k
0
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1
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75
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Dual equivalence of minimum feedback-vertex sets and cycle packing
it is known that the duals of feedback-set problems are set-packing problems; in the context of digraphs the feedback set are either a minimal set of vertices or edges that hit every oriented cycle; t …
- 13.2k
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0
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125
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Pitfalls with modeling problems as graphs
The motivation for this question is that I could solve problem by extracting a graph structure from it and then applying a standard graph-algorithm and transfering the solution back to the interpretat …
- 13.2k
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1
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40
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Reconstructing a 2-factor from its edge set
Let $G(V,E)$ be a symmetric graph with $n$ vertices and $m$ edges that has a $2\text{-factor}$ with edge set $F$, i.e. $F$ are the edges of an undirected vertex-disjoint cycle cover of $G$.
Question:
…
- 13.2k
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Subtour-gluing constraints for ILP formulation of TSPs
If one doesn't want to introduce additional variables to the ILP of a TSP instance, one has to add exponentially many so-called subtour-elimination constraints; in practical calculations subtour-elimi …
- 13.2k
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0
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76
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Regular graphs without non-trivial $f$-factor
Question:
are there any known examples of $k$-regular graphs that have no regular $f$-faktor, $1\le f\lt k;\ k\ge 3$, resp., can their existence or nonexistence be proved?
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