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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.
1
vote
1
answer
267
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History of the Vertex Disjoint Cycle Cover with Minimal Edgeweight Sum
Questions:
who first posed the problem of determining a collection of (directed) cycles, whose edgeweight sum is minimal and, for which each vertex belongs to exactly one of the cycles?
who came up …
- 13.2k
2
votes
0
answers
28
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Graph of the optimal spanning trees of a complete weighted graph
Given a complete weighted graph $G(V,E);\ E=\lbrace\lbrace u,v\rbrace\,|\,u,v\in V\rbrace$, the set $\mathbb{T}$ of the spanning trees of $G$ is the disjoint union of sets of spanning trees, whose und …
- 13.2k
0
votes
1
answer
37
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Graph connectivity after deleting an f-factor
Let $G(V,E)$ be an undirekted $k$-vertex-connected, $k$-regular graph
and let $F$ be an $f$-factor of $G$ consisting of a set of $f$-vertex-connected components, $f<k$.
Question:
what is the v …
- 13.2k
1
vote
3
answers
109
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Freely accessible collections of graph data
This question aims at providing links to definitions of graphs that either come from real-world problem or research that can be accessed and used freely; good examples in that vein are TSPLIB95 or the …
- 13.2k
11
votes
1
answer
390
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Shortest Paths in the "Cantor Graph"
First, let me explain, what I understand by a "Cantor Graph":
it is an infinite, directed graph with self loops and countably many vertices labelled with the natural numbers; every ordered pair of …
- 13.2k
1
vote
0
answers
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
-1
votes
1
answer
73
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Effect of a Specific Restriction on the Integrality of Min-cost Flow Solutions
I want to model the following situation: there is one production site (modelled by the source), a collection of depots (modelled by nodes without demand) and, of course many more customers (modelled b …
- 13.2k
2
votes
1
answer
1k
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Detecting Negative Cycles in Undirected Graphs
I recently faced the problem of quickly detecting negative cycles in undirected, weighted graphs. Resorting to the Bellman-Ford Algorithm, as commonly suggested, turned out to be very inefficient and …
- 13.2k
0
votes
0
answers
40
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Subgraph induced by negative cycles detected by Bellman-Ford algorithm
What is known about the properties of the subgraph induced by the negative cycles are defined by the predecessor relation that is established during the execution of the Bellman-Ford algorithm and arc …
- 13.2k
1
vote
0
answers
36
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Directed vertex-disjoint 3-cycle covers from Windy Postman tours?
It is a result of Zaw Win (paywall) that optimal Windy Postman tours in eulerian digraphs can be calculated in polynomial time.
Bodo Manthey has shown that directed 3-Cycle Covers are APX hard to appr …
- 13.2k
1
vote
1
answer
87
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Finding Optimal Vertex Weights without Linear Programing
Are there algorithms for finding $\omega_1\dots,\omega_n$, so that
$\omega_i+\omega_j\le \|e_{ij}\|\ \forall i,j\quad\wedge\quad\sum{\omega_i}=max$
that are not based on linear programing, e.g. …
- 13.2k
3
votes
1
answer
626
views
"Eccentricity" in the Definition of Graph Center
On the Wikepdia Page Graph Center I saw that the center of graph is the set of vertices with minimal eccentricity, i.e the set of vertices, whose maximal distance to other vertices is minimal.
On the …
- 13.2k
3
votes
1
answer
58
views
Name for Biconnected Tree+Cycle Graph
Is there an established name for graphs, that can be decomposed into
a tree with at least three leaf nodes and
a connected two-regular graph with the tree's leaf nodes as vertices?
examples of …
- 13.2k
2
votes
0
answers
38
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Can Orientability of Manifolds be Generalized to TSP Instances?
It is well known, that there are two basic kinds of manifolds, orientable and non-orientable ones; the most simple examples being obtained by identifying a pair of opposite sides of a rectangular stri …
- 13.2k
0
votes
0
answers
50
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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\quad\qu …
- 13.2k