Cycle Bases for Lattices of Binary Matroids with No Fano Dual Minor and Their One-Element Extensions

  title={Cycle Bases for Lattices of Binary Matroids with No Fano Dual Minor and Their One-Element Extensions},
  author={Tam{\'a}s Fleiner and Winfried Hochst{\"a}ttler and Monique Laurent and Martin Loebl},
  journal={J. Comb. Theory, Ser. B},
In this paper we study the question of existence of a basis consisting only of cycles for the lattice Z(M) generated by the cycles of a binary matroid M. We show that if M has no Fano dual minor, then any set of fundamental circuits can be completed to a cycle basis of Z(M); moreover, for any one-element extension M? of such a matroid M, any cycle basis for Z(M) can be completed to a cycle basis for Z(M?). 
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  • L. Goddyn
  • Mathematics, Computer Science
    Graph Structure Theory
  • 1991
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