# Undirected, Dense MST (Minimum Spanning Tree (MST))

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## Description

A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected; edge-weighted undirected graph that connects all the vertices together; without any cycles and with the minimum possible total edge weight. Here, we assume that the graph is dense (i.e. $E = \Omega(V)$).

## Related Problems

Generalizations: Undirected, General MST

Related: Undirected, Planar MST, Undirected, Integer Weights MST, Directed (Optimum Branchings), General MST, Directed (Optimum Branchings), Super Dense MST

## Parameters

$V$: number of vertices

$E$: number of edges

$U$: maximum edge weight

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Cheriton-Tarjan (dense) | 1976 | $O(E)$ | $O(E)$ auxiliary? | Exact | Deterministic | Time |