MIT6_042JF10_rec08

# MIT6_042JF10_rec08 - 6.042/18.062J Mathematics for Computer...

This preview shows pages 1–2. Sign up to view the full content.

6.042/18.062J Mathematics for Computer Science October 6, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 8 1 Build-up error Recall a graph is connected iﬀ there is a path between every pair of its vertices. False Claim. If every vertex in a graph has positive degree, then the graph is connected. 1. Prove that this Claim is indeed false by providing a counterexample. 2. Since the Claim is false, there must be a logical mistake in the following bogus proof. Pinpoint the Frst logical mistake (unjustiFed step) in the proof. Proof. We prove the Claim above by induction. Let P ( n ) be the proposition that if every vertex in an n -vertex graph has positive degree, then the graph is connected. Base cases : ( n 2). In a graph with 1 vertex, that vertex cannot have positive degree, so P (1) holds vacuously. P (2) holds because there is only one graph with two vertices of positive degree, namely, the graph with an edge between the vertices, and this graph is connected. Inductive

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

MIT6_042JF10_rec08 - 6.042/18.062J Mathematics for Computer...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online