Questions tagged [spanning-tree]
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65 questions
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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 opposite ...
- 3,587
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1
answer
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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 ...
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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 ...
- 323
6
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1
answer
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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 ...
- 4,422
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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 $A$...
- 6,962
3
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answer
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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?
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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 E_1\...
- 2,966
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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 ...
- 19
4
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1
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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 ...
- 43
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1
answer
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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 ...
- 723
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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 ...
- 6,962
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Minimum spanning tree of a random graph
Consider $n$ points arbitrarily located on the plane. Consider a random graph $G$ drawn from $G(n, \frac12)$ on these points (i.e. the Erdos-Renyi random graph where every edge is selected with ...
- 501
19
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4
answers
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Minimal graphs with a prescribed number of spanning trees
As it's long ago since Erdős died and MathOverflow is the second best alternative to him (for discussing personal problems), I'd like to start a fruitful discussion about the following problem that I ...
- 3,463
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Minimum spanning tree of a weighted graph
I have a connected graph $G=(V,E)$ in $n$ vertices. The edge weights are non-negative and form a metric space, thus for vertices $u,v,w \in V$ , such that $(u,v), (v,w), (w,u)\in E$ we have $r(u,w) \...
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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 ...
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