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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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159
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Heuristics for lightweighted "cubic" spanning trees
I have the problem of calculating a good approximation of the minimimum-weight spanning tree with vertex-degrees in $\lbrace 1,3\rbrace$ of a complete symmetric graph, without parallel edges or self-l …
CommunityBot
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1
vote
1
answer
79
views
Complexity of calculating the optimal amalgamation of an optimal cycle-cover
Let $G(V,E)$ be a complete symmetric graph with positive edge weights and let further $\mathcal{C}=\lbrace C_1,\,\cdots\,C_k\rbrace$ be the minimum-weight vertex-disjoint cycle cover.
The set $E$ of e …
CommunityBot
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1
answer
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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 $ …
- 5,429
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1
answer
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 …
CommunityBot
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4
votes
Accepted
Efficient algorithm for graph problem
If $v_1$ and $v_l$ are fixed then constructing a minimum weight breadth-first tree of height $l{-}1$ and finally optimally attach vertex $v_l$.
Iterating over all candidate pairs of $v_1$ and $v_l$ wo …
- 13.2k
2
votes
1
answer
328
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Worst case performance of heuristic for the non-Eulerian windy postman problem
The windy postman problem seeks the cheapest tour in a complete undirected graph, that traverses each edge at least once; the cost of traversing an edge is positive and may depend on the direction, in …
CommunityBot
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1
vote
1
answer
93
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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 $k$- …
CommunityBot
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6
votes
1
answer
368
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How does the complexity of calculating the Permanent imply the NP completeness of directed 3...
In their paper Two Approximation Algorithms for 3-Cycle Covers of Markus Bläser and Bodo Manthey it is stated that:
"...deciding whether an unweighted directed graph has a 3-cycle cover is already NP- …
- 13.2k
1
vote
Complexity of maximum weight-sum matching for cycle graphs
With inspiration from the comments I arrived at the following idea:
the maximum weight matching on the cycle is converted to a maximum weight matching on a path that is generated by splitting a vertex …
- 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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votes
0
answers
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
2
votes
1
answer
224
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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 …
- 24.2k
0
votes
Minimally 2-vertex-connected graphs?
$K_3$ is the only graph with a triangle that contains a bivalent vertex, and is a minimally vertex 2-connected graph (MV2CG).
According to the two ears theorem every triangulated polygon with at least …
- 13.2k
1
vote
Minimally 2-vertex-connected graphs?
I conjecture that a a sufficient condition for a graph being minimally 2-vertex-connected is that
it is $2$-vertex-connected and if every vertex $u$ is adjacent to some vertex $v$ of degree $2$ and c …
- 13.2k
0
votes
0
answers
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