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

Categorical variable, Categorical variable : A variable which provides the ...

Categorical variable : A variable which provides the appropriate label of observation after the allocation to one of the several possible categories, for instance, the respiratory

Fuzzy set theory, A radically different approach of dealing with the uncert...

A radically different approach of dealing with the uncertainty than the traditional probabilistic and the statistical methods. The necessary feature of the fuzzy set is a membershi

Spreading function and scattering function, 1)  Consider an antenna with a ...

1)  Consider an antenna with a pattern: G(θ,φ) = sinn(θ/θ0) cos(θ/θ0)   where θ0 = Π/1.5 (a) What is the 3-dB bandwidth? (b) What is the 10-dB beam width? (c) What is t

Factor scores, The values assigned to factors for the individual sample uni...

The values assigned to factors for the individual sample units in a factor analysis. The most common approach is "regression method". When the factors are seen as the random variab

Linear regression assignment help, Using World Bank (2004) World Developmen...

Using World Bank (2004) World Development Indicators; Washington: International Bank for Reconstruction & Development/ The World Bank, located in the reference section of the Learn

Dropout, A subject who withdraws from the study for whatever reason, advers...

A subject who withdraws from the study for whatever reason, adverse side effects, noncompliance, moving away from the district, etc. In number of cases the reason may not be known.

Calculate the probability, (a) A plane timetable states that a particular p...

(a) A plane timetable states that a particular plane is due at 2pm but the actual arrival time isuniformly distributed between 1pm and 3pm. (i) Calculate the probability that th

SCATTER DIAGRAM, MEANING ,IMPORTANCE AND RELEAVANCE OF SCATTER DIAGRAM

MEANING ,IMPORTANCE AND RELEAVANCE OF SCATTER DIAGRAM

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