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Given an undirected graph G = (V, E) in which each node has degree d, show how to
Chapter 9, Problem 9.4(choose chapter or problem)
Given an undirected graph G = (V, E) in which each node has degree d, show how to efficientlyfind an independent set whose size is at least 1/(d + 1) times that of the largest independent set.
Questions & Answers
QUESTION:
Given an undirected graph G = (V, E) in which each node has degree d, show how to efficientlyfind an independent set whose size is at least 1/(d + 1) times that of the largest independent set.
ANSWER:Step 1 of 2
A tree on nodes has \(m-1\) edges as you say. However, also guaranteed for a tree is that there are 2 or more nodes with degree of 1, which is excluded here. You can also demonstrate the existence of a circuit by constructing a path from the start node and then continuing to follow random edges (using the condition given that no node has degree 1) until you revisit some node, implying a circuit.