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

Define model, Model is the description of the supposed structure of a set ...

Model is the description of the supposed structure of a set of observations which can range from a fairly imprecise verbal account to, more commonly, a formalized mathematical exp

Change point problems, Change point problems : Problems with chronologicall...

Change point problems : Problems with chronologically ordered data collected over the period during which there is known to have been a change in the underlying data generation cou

Generalized additive model, The linear component ηi, de?ned just in the tra...

The linear component ηi, de?ned just in the traditional way: η i = x' 1 A monotone differentiable link function g that describes how E(Yi) = µi is related to the linear compon

Explain maternal mortality, Maternal mortality : The maternal death is the ...

Maternal mortality : The maternal death is the death of a woman while pregnant, delivering a baby or within 42 days of the termination of pregnancy, from any reason related to or a

Business forcastin.., elements , importance, limitation, and theories

elements , importance, limitation, and theories

Statistical methods with financial applications, The marketing manager of H...

The marketing manager of Handy Foods Ltd. is concerned with the sales appeal of one of the company's present label for one of its products. Market research indicates that supermark

Daycare, facts and statistics about daycare

facts and statistics about daycare

Drug stability studies, The studies conducted in the pharmaceutical industr...

The studies conducted in the pharmaceutical industry to calculate the degradation of the new drug product or an old drug formulated or packaged in the new manner. The main study ob

Historigram, difference between histogram and historigram

difference between histogram and historigram

Probability, Modern hotels and certain establishments make use of an electr...

Modern hotels and certain establishments make use of an electronic door lock system. To open a door an electronic card is inserted into a slot. A green light indicates that the doo

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