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Questions tagged [spanning-tree]

A spanning tree in an connected, undirected graph is a subgraph that includes all vertices, is a tree and is connected.

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Spanning Tree that Preserves the Number of Branch Vertices

Suppose a undirected connected graph $G$, denote the number of vertices in $G$ as $n$, number of branch vertices (i.e., vertices with degree $\geq 3$) as $n_{\geq 3}$. Suppose $n_{\geq 3}>\log(n)$. My question is: Is there always a spanning tree $T$…
Mingzhou Liu
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is it possible to find a spanning tree for a direct and unweighted graph?

I try to explain my problem better. in input I have the number of nodes N and the number of edges P. N represent the cities while P the water pipes. So for example in input I have 4 and 2 {0,1,2,3,4} would be my graph and the 2 represents me the…
mimmolg99
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Is the computed number of spanning trees for this undirected graph reasonable/correct?

This is part of my Master thesis which is about designing hydrogen pipeline networks. For a particular graph of 135 nodes and 157 edges and (see figure below), I need to compute the number of spanning trees (spanning all nodes). I used the…
Khalilbs
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How is a cut lonely if there are often multiple edges crossing a cut in a connected undirected graph?

I'm learning the requirements for finding a minimum spanning tree for a connected, undirected graph with distinct edge costs. One of the requirements is that there must be no cycles created in the tree, and the reason given for why a cycle isn't…
julieb
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Time Complexity of (Minimum Spanning Tree) Prim's Algorithm

When we implement this algorithm using adjacency matrix and without using priority queue, the time complexity comes out to be O(V^2), where V is the total no. of vertices and E is the total no. of edges. But when we implement it using priority…
Dhrxv
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Edmond maximum branching algorithm

I am trying to have an implementation on Python for Edmond's maximum branching algorithm. Maximum Branching Problem. Given a directed graph G=(V,E, w) where w be the weight function. For a root r in V, determine a branching G'=(V,E') rooted r, i.e.…
The Nguyen
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Ne04j Graph Nodes, Expand a spanning tree but stop at specific node (but don't stop for other nodes)

I have the following setup Person is part of an organisation Person attends meeting Meeting is held in a location More than one person can attend a meeting More than one person can be part of same organisation Persons from different organisation…
Bertrand Leroy
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How to find a spanning tree of a undirected graph(not necessary MST)?

I know the brute force approach for solving this problem which can be given as: Iterate over all edges Take a set(or list)(suppose s) if adding an edge to s doesn't make a cycle then add edge to s End if iteration is complete over all edges. But I…
Abhishek Jaiswal
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Minimum spanning trees of sub-graphs?

Any hint please if I should prove or search for counterexample, at least to know which direction to go... Consider the following 2 graphs: G1 (V, E1) G2 (V, E2) and a weight function for the vertices w: (E1 \untion E2) -> R and 2 minimum spanning…
user15862679
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Counting spanning trees in a graph

I have a problem. I am trying to count all the spanning trees in a graph(it doesn't have multi edges). I know that there is Kirchhoff's theorem, which lets me count it in quite an easy way, but I prefer a solution which uses cycles in this graph. I…
manez
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Give me an example of why IP tries to route on a spanning tree

I've been watching a talk given by Van Jacobson in which he casually claims that IP tries to route on a spanning tree, as not doing so results in loops which can quickly bring down a network. He then goes on to say that one of the disadvantages…
Bryce Thomas
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Maximum spanning tree using Prim's algorithm

How would this algorithm be changed to give a maximum spanning tree? MST_prim(G,w,r) for each u that exists in G.V u.key= inf u.pi=NIL r.key=0 Q=G.V While Q is not empty u= EXTRACT-MIN(Q) for each v in G.Adj[u] if v is in Q and…
Mia Sheikh
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Configure STP protocol via scapy

I need to generate and STP traffic using scapy and when I visualize it via wireshark I get an output similar to the caption shown below: when I run this code: from scapy.all import STP import scapy from scapy.all import…
newbie
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Given an unweighted graph how do I find a spanning tree with 1. Maximum number of leaves 2 minimum number of leaves

write an algorithm to find a spanning tree that has the maximum number of leaves. Write an algorithm to find a spanning tree with minimum number of nodes. I am yet not able to come up with a solution for the following questions. For the first…
Prateek Agrawal
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Show that there exists a minimum spanning tree from a vertex always containing the shortest edge from that vertex

Suppose that e is an edge in a weighted graph that is incident to a vertex v such that the weight of e does not exceed the weight of any other edge incident to v. Show that there exists a minimum spanning tree containing this edge.
Dhruv Pathak
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