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

Normality - reasons for screening data, Normality - Reasons for Screening...

Normality - Reasons for Screening Data Prior to analyzing multivariate normality, one should consider univariate normality Histogram, Normal Q-Qplot (values on x axis

Baddeley''smetric, Baddeley'smetric : A manner of measuring the 'error' in ...

Baddeley'smetric : A manner of measuring the 'error' in the image processing technique or method. The metric is derived using the fundamental theory from the stochastic geometry an

Multimodal distribution, what is pdf,mean & variance for multimodal distrib...

what is pdf,mean & variance for multimodal distribution?

Please answer this question, How large would the sample need to be if we ar...

How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;

Hypothesis testing, Hypothesis testing is a  general term for procedure of...

Hypothesis testing is a  general term for procedure of assessing whether the sample data is consistent or otherwise with statements made about the population. It basically tells u

Define non linear mapping (nlm), Non linear mapping (NLM ) is a technique f...

Non linear mapping (NLM ) is a technique for obtaining a low-dimensional representation of the set of multivariate data, which operates by minimizing a function of the differences

Line-intersect sampling, Line-intersect sampling is a technique of unequal...

Line-intersect sampling is a technique of unequal probability sampling for selecting the sampling units in the geographical area. A sample of lines is drawn in a study area and, w

Explain knox''s test, Knox's tests: These tests designed to detect any ten...

Knox's tests: These tests designed to detect any tendency for the patients with a particular disease to form the disease cluster in time and space. The tests are relied on a two-b

Principal components analysis, Principal components analysis is a process ...

Principal components analysis is a process for analysing multivariate data which transforms original variables into the new ones which are uncorrelated and account for decreasing

Glejser’s test, The Null Hypothesis - H0:  There is no heteroscedasticity i...

The Null Hypothesis - H0:  There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1:  There is heteroscedasticity i.e. β 1 0 Reject H0 if |t | > t = 1.96

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