This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: vertices. (Vertex v j precedes v i if j < i .) Use induction to prove that every graph with width at most w is ( w + 1)colorable. (Recall that a graph is kcolorable i every vertex can be assigned one of k colors so that adjacent vertices get dierent colors.) 3 Problem 2 A planar graph is a graph that can be drawn without any edges crossing. 1. First, show that any subgraph of a planar graph is planar. 2. Also, any planar graph has a node of degree at most 5. Now, prove by induction that any graph can be colored in at most 6 colors. MIT OpenCourseWare http://ocw.mit.edu 6.042J / 18.062J Mathematics for Computer Science Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
View
Full
Document
 Fall '10
 TomLeighton,Dr.MartenvanDijk
 Computer Science

Click to edit the document details