{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# ps9 - Introduction to Algorithms Massachusetts Institute of...

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

Introduction to Algorithms December 6, 2002 Massachusetts Institute of Technology 6.046J/18.410J Professors Erik Demaine and Shafi Goldwasser Handout 31 Problem Set 9 (Optional) This problem set is not due; it is optional. Reading: Chapter 34 Problem 9-1. Prove that the following problems are in : (a) there exists a simple path in between and , of length at least (b) it is possible to assign one of three “colors” to each vertex of such that no two neighboring vertices are assigned the same color Problem 9-2. A subgraph of a graph is a graph where ; i.e. it is a subset of the vertices together with all the edges of the original graph which are incident to these vertices. Consider the problem L ARGEST C OMMON S UBGRAPH : Given two graphs and and an inte- ger , determine whether there is a graph with edges which is a subgraph of both and . ( Hint: Reduce from C LIQUE .) Problem 9-3. A perfect matching in an undirected graph is a collection of edges such that each node has exactly one edge of incident to it. (In other words, the degree of each

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 ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern