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.
|Title of host publication||Proceedings - IEEE International Symposium on Circuits and Systems|
|Number of pages||4|
|Publication status||Published - 1985|
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials