On Mills's conjecture on matroids with many common bases |
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Authors: | Manoel Lemos |
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Institution: | Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Pernambuco, 50.740-540, Brazil |
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Abstract: | In this paper, we shall prove a conjecture of Mills: for two (k+1)-connected matroids whose symmetric difference between their collections of bases has size at most k, there is a matroid that is obtained from one of these matroids by relaxing n1 circuit-hyperplanes and from the other by relaxing n2 circuit-hyperplanes, where n1 and n2 are non-negative integers such that n1+n2k |
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