Graphs II: Basic Algorithms :

Minimum Spanning Tree (MST)

•  Problem: Given a weighted undirected graph G, find the minimum spanning tree.
• One of the main property of a tree is cycle freeness.
• This property is exploited during construction of a MST for a given graph. That is, to obtain an spanning tree of a given graph, start from a null graph add edges one after the other without forming cycles.
• If the edges considered for adding is in the increasing order we get a MST.
• Consider the following weighted graph.