The spanning-tree tag has no wiki summary.

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### Euclidean Minimum Spanning Trees Restricted to One Vertex Per Grid Cell

Given an $n \times n$ grid with unit grid cells, and one point from the interior
of each cell, what is are best possible lower and upper bounds for lengths of minimum spanning trees? The lower bound ...

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**0**answers

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### Characterizing graphs with $k$ edge-disjoint minimum diameter spanning trees

Henneberg [1] and Laman [2] characterized graphs which have, after adding any edge, 2 edge-disjoint spanning trees. This was generalized to $k$ edge-disjoint spanning trees by Frank and Szegõ [3]. ...

**2**

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**1**answer

130 views

### Maximum number of hyperedges on a hypergraph without a spanning tree

Although every connected graph has a spanning tree, the same is not true for hypergraphs: consider the hypergraph on 4 vertices with all possible edges of size 3. You need to pick at least two edges ...

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### On some special spanning trees of grid graphs

I would like to know if there are existing results on the following objects:
spanning trees of a grid graph, with no corridor
where a corridor is a vertex having exactly two neighbors, on ...

**5**

votes

**1**answer

278 views

### Minimum Spanning Tree of Graph with Unknown Weights

I have a fully connected graph $G=(V,E)$ with $n$ vertices. The edge weights $w(e)$ with $e\in E$ are non-negative and form a metric space (e.g. Hamming distance), thus for vertices $v,u,y \in V$, we ...

**12**

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**4**answers

920 views

### Graphs in which every spanning tree is an independency tree

It follows from this question
and the corresponding answers, that the complete graphs and the cycles are precisely the graphs
$G$ having the property that, for every spanning tree $T$ of $G$, the ...

**6**

votes

**1**answer

293 views

### Random path in a graph

Consider a finite graph $G$. I would like to define a random path between two vertices $s$ and $t$ of the graph $G$ by looking at a measure $\mu$ on all spanning trees. Then the probability of a given ...

**3**

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**0**answers

142 views

### Matrix-tree for matrices with constant diagonal

I've got a symmetric matrix $A$ whose entries are in $\{0,-1,1\}$, with the diagonal entries all equal to $1$. I'm interested in finding a combinatorial description of the entries of the inverse of ...

**3**

votes

**1**answer

87 views

### rainbow spanning tree

In graph G, every edge has a color. Rainbow spanning tree is a spanning tree where all edges have different colors.
I want a polynomial algorithm to find such tree if exists any
Anyone can help?

**2**

votes

**0**answers

289 views

### Incremental minimum spanning tree

Given a connected graph $G=(V,E)$ with a weight function $w:E\to\mathbb{R}$ and a subset $E_0\subseteq E$ such that the subgraph $(V,E_0)$ is connected, I am looking for a sequence $E_0\subseteq ...

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votes

**3**answers

265 views

### Minimize diameter of a tree

Hi! I have an acyclic undirected unweighted connected graph (a tree :) ), and I have to disconnect an edge and create a new one to minimize the diameter.
For now, I do a bfs on a arbitrary node, find ...

**4**

votes

**1**answer

176 views

### Divisibility Relation for Spanning Trees of a Graph

Let $A = \big[{1\ 1\atop 1\ 0}\big]$, and let $G_n$ be the graph whose adjacency matrix is
$A^{\otimes n}$. Also let $\kappa(G)$ denote the number of spanning trees of $G$. From a significant amount ...

**1**

vote

**1**answer

375 views

### Minimum spanning subgraph with at least one incoming and one outgoing edge

Given a single-component, directed acyclic graph with one source (vertex with only outgoing edges) and one sink (vertex with only incoming edges), I'd like to find a minimum spanning subgraph which ...

**3**

votes

**1**answer

429 views

### How random are random spanning trees?

Suppose you take a $G(n,p)$ random graph for a fixed probability $p$ and find a spanning tree using Kruskal's algorithm. If you now repeat this process indefinitely, will every tree on $n$ vertices ...

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vote

**1**answer

2k views

### 3D Delaunay Triangulation -> Euclidean Minimum Spanning Tree

I read that the Euclidean Minimum Spanning Tree (EMST) of a set of points is a subgraph of any Delaunay triangulation. Apparently the easiest/fastest way to obtain the EMST is to find the Deluanay ...