### Abstract

The problem of finding the principal partition of a parity matroid is shown to be polynomially unsolvable in general. Two theorems are refined by using the concept of a minimal central minor: the first is the theorem on the existence of the principal partition; the second is the theorem on the characterization of the maximum independent parity set of a matroid with principal partition. A new polynomially solvable class of the parity problem is presented. Also, the weighted parity problem of a matroid with a principal partition is shown to be polynomially unsolvable in general. Finally, the concept of the principal partition for a parity matroid is generalized to a parity polymatroid.

Original language | English |
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Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Publisher | IEEE |

Pages | 815-818 |

Number of pages | 4 |

Publication status | Published - 1985 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(pp. 815-818). IEEE.

**REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM.** / Onozawa, Akira; Inoue, Masayuki; Oishi, Shinichi; Horiuchi, Kazuo.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE International Symposium on Circuits and Systems.*IEEE, pp. 815-818.

}

TY - GEN

T1 - REFINEMENT OF THE CONCEPT OF PRINCIPAL PARTITION FOR MATROID PARITY PROBLEM.

AU - Onozawa, Akira

AU - Inoue, Masayuki

AU - Oishi, Shinichi

AU - Horiuchi, Kazuo

PY - 1985

Y1 - 1985

N2 - The problem of finding the principal partition of a parity matroid is shown to be polynomially unsolvable in general. Two theorems are refined by using the concept of a minimal central minor: the first is the theorem on the existence of the principal partition; the second is the theorem on the characterization of the maximum independent parity set of a matroid with principal partition. A new polynomially solvable class of the parity problem is presented. Also, the weighted parity problem of a matroid with a principal partition is shown to be polynomially unsolvable in general. Finally, the concept of the principal partition for a parity matroid is generalized to a parity polymatroid.

AB - The problem of finding the principal partition of a parity matroid is shown to be polynomially unsolvable in general. Two theorems are refined by using the concept of a minimal central minor: the first is the theorem on the existence of the principal partition; the second is the theorem on the characterization of the maximum independent parity set of a matroid with principal partition. A new polynomially solvable class of the parity problem is presented. Also, the weighted parity problem of a matroid with a principal partition is shown to be polynomially unsolvable in general. Finally, the concept of the principal partition for a parity matroid is generalized to a parity polymatroid.

UR - http://www.scopus.com/inward/record.url?scp=0022306706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022306706&partnerID=8YFLogxK

M3 - Conference contribution

SP - 815

EP - 818

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - IEEE

ER -