Geodesic
The structure of binary matroids with no induced claw or Fano plane restriction
Advances in Combinatronics (2019)

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An 'induced restriction' of a simple binary matroid $M$ is a restriction $M|F$, where $F$ is a flat of $M$. We consider the class $\mathcal{M}$ of all simple binary matroids $M$ containing neither a free matroid on three elements (which we call a 'claw'), nor a Fano plane as an induced restriction. We give an exact structure theorem for this class; two of its consequences are that the matroids in $\mathcal{M}$ have unbounded critical number, while the matroids in $\mathcal{M}$ not containing the clique $M(K_5)$ as an induced restriction have critical number at most $2$.
Publié le : 
@article{ADVC_2019_a4,
     author = {Marthe Bonamy and Frantisek Kardos and Tom Kelly and Peter Nelson and Luke Postle},
     title = {The structure of binary matroids with no induced claw or {Fano} plane
  restriction},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2019_a4/}
}
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Marthe Bonamy; Frantisek Kardos; Tom Kelly; Peter Nelson; Luke Postle. The structure of binary matroids with no induced claw or Fano plane
  restriction. Advances in Combinatronics (2019). http://geodesic.mathdoc.fr/item/ADVC_2019_a4/