Petersen''s factor theorem, Advanced Statistics

Assignment Help:

Suppose the graph G is n-connected, regular of degree n, and has an even number of vertices. Prove that G has a one-factor.

Petersen's 2-factor theorem (Theorem 5.40 in the notes) proves that every regular graph G of even degree has a 2-factor by nding a 1-factor in a regular bipartite graph which is constructed from an Eulerian trail of G. However, the choice of Eulerian trail and 1-factor determines which 2-factor is obtained. Consider the following Eulerian trail C of K7 where V (K7) = {0; 1; 2; 3; 4; 5; 6}.

C : 0; 1; 2; 3; 4; 5; 6; 0; 2; 4; 6; 1; 3; 5; 0; 3; 6; 2; 5; 1; 4; 0:

(a) List a 2-factor of K7 of type [3; 4] that could arise from C via the proof technique of Petersen's theorem, and explain why it could arise.

(b) List a 2-factor of K7 that could not arise from C via the proof technique of Petersen's theorem, and explain why it could not arise.


Related Discussions:- Petersen''s factor theorem

Histogram, Histogram is the graphical representation of the set of observat...

Histogram is the graphical representation of the set of observations in which class frequencies are represented by the regions of rectangles centred on the class interval. If the f

Degenerate distributions, The special cases of the probability distribution...

The special cases of the probability distributions in which the random variable's distribution is concentrated at one point only. For instance, a discrete uniform distribution when

Define recurrence risk, Recurrence risk : Usually the probability that an i...

Recurrence risk : Usually the probability that an individual experiences an event of interest given previous experience(s) of the event; for example, the probability of recurrence

Efficiency, This term applied in the context of comparing the different met...

This term applied in the context of comparing the different methods and techniques of estimating the same parameter; the estimate with the lowest variance being regarded as the mos

Prepare a depreciation schedule for the rental equipment, Sam Tyler, a sing...

Sam Tyler, a single taxpayer, social security number 111-44-1111, bought Rental Equipment on 04/01/2010. He paid $400,000 including all closing and delivery costs. In the current y

Regression analysis, The regression analysis is used to fit a model descr...

The regression analysis is used to fit a model describing the relationship of a dependent variable with independent variable(s). Here we have fitted three regression models:

Bootstrap, Bootstrap : The data-based simulation method/technique for the s...

Bootstrap : The data-based simulation method/technique for the statistical inference which can be used to study the variability of the estimated characteristics of the probability

Fisher''s scoring method, This is an alternative to the Newton-Raphson tech...

This is an alternative to the Newton-Raphson technique for optimization (finding out the minimum or the maximum) of some function, which includes replacing the matrix of second der

Random success probability, a psychic claims to be able to "feel colors" th...

a psychic claims to be able to "feel colors" there are three pieces of colored paper(red, blue,green) he will place his hand on radomly selected pieces while blindfolded. you perfo

Operations Management, 1.Sam Lucarelli, owner of Lucarelli Products, is eva...

1.Sam Lucarelli, owner of Lucarelli Products, is evaluating whether to produce a new product line. After thinking through the production process and the costs of raw materials and

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