Questions tagged [spanning-tree]

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27 views

Finding the smallest-cost way to deliver goods

I want to deliver products from various sources to various destinations such that the overall cost is minimized. We need to deliver these products while obeying our contractual obligatione with each ...
6
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0answers
105 views

Enumerating homologies of disjoint paths

I am reading this recent paper by Schrijver, in particular, section 4.2: Enumerating homologies of disjoint paths. I did not understand how do they re-route the paths through a spanning tree and ...
2
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1answer
102 views

NP-completeness: sum of “some” paths in a spanning tree

I suspect this problem is NP-complete but I couldn't prove it, if anyone can help I'll be very grateful: Instance: undirected, unweighted, connected graph $G=(V,E)$, positive integer $K \in \mathbb{Z}...
2
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0answers
76 views

Variation of edge-disjoint spanning trees

In a directed graph, I want to find 2 edge-disjoint spanning trees (arborescence), with the extra restrictions that edges in the 1st tree are not forward arcs in the 2nd tree. Are there existing ...
1
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1answer
60 views

Are there digraphs such that any two arborescences are arc-disjoint?

Let $D=(V,A)$ be a directed graph with root $r$. An $r$-arborescence of $D$ is a subgraph such that for any $v\in V-r$, there is exactly one directed path from $r$ to $v$. Hence an $r$-arborescence is ...
8
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0answers
181 views

How to sample a lot of independent uniform spanning trees?

There are a bunch of good algorithms for sampling a uniform spanning tree from a graph $G$. For example, Aldous/Broder and Wilson's algorithm are pretty efficient. However, each of these graphs only ...
5
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2answers
181 views

Minimising the root-set of a spanning hyperforest of a hypergraph

I am interested in the complexity of a problem involving spanning hyperforests (a union of hypertrees, which covers all of the vertices) of a $k$-hypergraph. I describe the relevant definitions for ...
2
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1answer
68 views

Are equally weighted MSTs closely related?

Suppose we have an undirected connected graph $G=(V,E)$ that has several minimum spanning trees. We say two trees $T_1, T_2$ are connected if they share exactly $|V|-2$ edges(*). In other words $T_1$ ...
4
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0answers
149 views

Girth of graphs that decompose into two disjoint union of spanning trees

Let $G$ be an $n$-node graph that can be decomposed into two disjoint union of spanning trees. In particular, $G$ has $2n-2$ edges. It is not hard to show that the girth of $G$ is at most $O(\log n)...