Improved bound for the Carathéodory rank of the bases of a matroid

Authors:
José Coelho de Pina;José Soares
Affiliations:
Departamento de Ciencia da Computacao, Instituto de Matematica e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil;Departamento de Ciencia da Computacao, Instituto de Matematica e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508-090 São Paulo, Brazil
Venue:
Journal of Combinatorial Theory Series B
Year:
2003

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Abstract

Let M be a matroid on m elements and let r be its rank. We show that any vector in the integer cone of the incidence vectors of bases of M can be written as nonnegative integer combination of at most m + r - 1 incidence vectors of bases of M.