IsMinorOf - Maple Help
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Matroids

  

IsMinorOf

  

determine if a given matroid is a minor of another

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

IsMinorOf(M1,M2)

IsMinorOf(M1,M2,mo,oo)

Parameters

M1

-

Matroid

M2

-

Matroid

mo

-

(optional) equation of the form maxiterations=m, where m is a positive integer or the symbol

oo

-

(optional) equation of the form output=o

Description

• 

A matroid M1 is a minor of another matroid M2 if M1 can be obtained from M2 via a sequence of deletion and contraction operations. This procedure determines if M1 is a minor of M2.

• 

In some cases, this question can be decided quickly, e.g., if M1 has more entries in its ground set than M2, the answer is no. Otherwise, this command enters into a loop that can take quite a long time to run. By default, Maple will issue an error message if it computes that the loop may take more than 220 iterations. To use a different limit for the current call, you can supply the option maxiterations=m, where m is either a positive integer or the symbol .

• 

By default, if M1 is not a minor of M2, this command returns the value false. If M1 is indeed a minor of M2, it returns a sequence of three values: the constant true and two subsets C and D of the ground set of M2 such that M1 is isomorphic to M2D/C. The output can be modified using an option of the form output=o.

– 

If you pass the option output=boolean, the command returns just true or false.

– 

If you pass the option output=contractions, the command returns just C if M1 is a minor of M2, and the symbol FAIL otherwise.

– 

If you pass the option output=deletions, the command returns just D if M1 is a minor of M2, and the symbol FAIL otherwise.

– 

If you pass the option output=l, where l is a list consisting of any of the values boolean, contractions, and deletions, the command returns an expression sequence of the corresponding outputs in the given order.

– 

If you pass the option output=default, the command behaves as if the option had not been passed.

Examples

withMatroids:

withExampleMatroids:

Let us verify that the uniform matroid of rank 1 on 2 elements is a minor of the Fano matroid.

M1UniformMatroid1,2

M1thⅇ unⅈform matroⅈⅆ of rank 1 on 2 ⅇlⅇmⅇnts

(1)

M2Fano

M2a matroⅈⅆ on 7 ⅇlⅇmⅇnts wⅈth 14 cⅈrcuⅈts

(2)

IsMinorOfM1,M2

true,4,3,5,6,7

(3)

We can verify the answer as follows.

M3ContractionDeletionM2,3,5,6,7,4

M3thⅇ unⅈform matroⅈⅆ of rank 1 on 2 ⅇlⅇmⅇnts

(4)

AreIsomorphicM1,M3

true

(5)

References

  

James G. Oxley. Matroid Theory (Oxford Graduate Texts in Mathematics). New York: Oxford University Press. 2006.

See Also

Matroids[AreIsomorphic]

Matroids[Contraction]

Matroids[Deletion]