Show that the vector is in the perfect matching polytope, Mathematics

Assignment Help:

1.  Let G = (V,E) be a graph for which all nodes have degree 5 and where G is 5-edge is connected.

a) Show that the vector x which is indexed by the edges E and for which xe = 1/5 for all e in E is in the Perfect Matching Polytope PPM.

b)  Use your result in a) to show that G must have a perfect matching.

c) Show that b) may not be true if G is only 1-edge connected (but still has degree 5 everywhere) by giving an example of such a graph G which has no perfect matching.


Related Discussions:- Show that the vector is in the perfect matching polytope

Matrix addition and subtraction, What is Matrix addition and subtraction? I...

What is Matrix addition and subtraction? Illustrate the procedure of Matrix addition and subtraction.

Pi, is that rational or irrational number

is that rational or irrational number

What is the opec, What is the OPEC? - The Organization of the Petroleum Exp...

What is the OPEC? - The Organization of the Petroleum Exporting Countries, a coordination group of petrol producers The Organization for Peace and Economic Cooperation, a German le

Systems of linear equation, a man can row a bangka at a rate of 5 km/h in s...

a man can row a bangka at a rate of 5 km/h in still water. It takes 10 minutes longer to row upstream a distance of 2km than he takes to row downstream. What is the rate of the cur

Find out that the relation is an equivalent relation or not, Let m be a pos...

Let m be a positive integer with m>1. Find out whether or not the subsequent relation is an equivalent relation. R = {(a,b)|a ≡ b (mod m)} Ans: Relation R is illust

Set builder notation, A={2,3,5,7,11} B={1,3,5,7,9} C={10,20,30,40,......100...

A={2,3,5,7,11} B={1,3,5,7,9} C={10,20,30,40,......100} D={8,16,24,32,40} E={W,O,R,K} F={Red,Blue,Green} G={March,May} H={Jose,John,Joshua,Javier} I={3,6,9,12,15}

Calculate the volume of rectangular piece of cardboard, 1. A rectangular pi...

1. A rectangular piece of cardboard measuring 15 inches by 24 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side

Ratios, a doctor sees 3 boys to 5 girls in one week . If he sees 40 boys in...

a doctor sees 3 boys to 5 girls in one week . If he sees 40 boys in one day then how many girls does he see that day

Tangents, two circle of radius of 2cm &3cm &diameter of 8cm dram common tan...

two circle of radius of 2cm &3cm &diameter of 8cm dram common tangent

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd