PS03-100225 - MATH 682 Problem Set #3 This problem set is...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
MATH 682 Problem Set #3 This problem set is due at the beginning of class on February 25 . Below, “graph” means “simple finite graph” except where otherwise noted. 1. (15 points) Demonstrate the following facts about a directed graph D . (a) (5 points) Prove that sum v V ( D ) d - D ( v ) = v V ( D ) d + D ( v ). Recall that d - and d + represent the indegree and outdegree respectively. (b) (10 points) Prove that a directed Eulerian tour (i.e. a directed closed trail traversing every edge) exists if and only if d - ( v ) = d + ( v ) for all v V ( D ). 2. (10 points) Suppose each edge in a digraph D with a source s and sink t has not only a maximum capacity c ( e ) but also a minimum required flow b ( e ), so that a flow f must satisfy b ( e ) f ( e ) c ( e ). Assume we know of a legal but not necessarily maximal flow f 0 . Explain how the Ford-Fulkerson algorithm could be modified to produce a maximum flow under these constraints. 3.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/12/2012 for the course MATH 682 taught by Professor Wildstrom during the Spring '09 term at University of Louisville.

Ask a homework question - tutors are online