Geodesic
There are only a finite number of excluded minors for the class of bicircular matroids
Advances in Combinatronics (2023)

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We show that the class of bicircular matroids has only a finite number of excluded minors. Key tools used in our proof include representations of matroids by biased graphs and the recently introduced class of quasi-graphic matroids. We show that if $N$ is an excluded minor of rank at least ten, then $N$ is quasi-graphic. Several small excluded minors are quasi-graphic. Using biased-graphic representations, we find that $N$ already contains one of these. We also provide an upper bound, in terms of rank, on the number of elements in an excluded minor, so the result follows.
Publié le : 
@article{ADVC_2023_a0,
     author = {Matt DeVos and Daryl Funk and Luis Goddyn and Gordon Royle},
     title = {There are only a finite number of excluded minors for the class of
  bicircular matroids},
     journal = {Advances in Combinatronics},
     publisher = {mathdoc},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2023_a0/}
}
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Matt DeVos; Daryl Funk; Luis Goddyn; Gordon Royle. There are only a finite number of excluded minors for the class of
  bicircular matroids. Advances in Combinatronics (2023). http://geodesic.mathdoc.fr/item/ADVC_2023_a0/