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《Mathematics in Practice and Theory》 2013-17
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(F-Z_1)-flowable Matroid(M-Z_1)/Z_2 in 1/2Z~

L Guo-liang;YU Bao-min;Department of Mathematics and Information Science,Weinan Teachers University;  
Some properties of minors of F-flowable matroid in 1/2Z~+ are investigated.The definition of F-flowable matroids in 1/2Z~+ and necessary and sufficient conditions that a matriod is F-flowable are given.It is proved that if a matroid has no loop elements,then its every element is contained in the k minimum coircuits.For a set of minimum circuits satisfying certain conditions,there exist an equality of minimum sets of minimum circuits.For a function p' in minors satisfying inequality of(F-Z_1)-flowable matroid in 1/2Z~+,defined p by p',it is proved that p also satisfy the same inequaUty.From the function Φ which satisfying the equality of F-flowable matroids,the minimum circuits belongs to minors can be found,defined Φ'(C') and then,it can be showed that Φ' satisfy the(F-Z_1)-flowable equality in 1/2Z~+.By the sufficient and necessary conditions of F-flowable in 1/2Z~+,the(F-Z_1)-flowability of minors(M-Z_1)/Z_2 in 1/2Z~+ is proved.
【Fund】: 陕西省教育厅自然科学基金(12JK0866)
【CateGory Index】: O151.21
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