Geodesic
There are only a finite number of excluded minors for the class of bicircular matroids
Advances in Combinatorics (2023)
Cet article a éte moissonné depuis la source Scholastica

Voir la notice de l'article

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 Combinatorics},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADVC_2023_a0/}
}
TY  - JOUR
AU  - Matt DeVos
AU  - Daryl Funk
AU  - Luis Goddyn
AU  - Gordon Royle
TI  - There are only a finite number of excluded minors for the class of bicircular matroids
JO  - Advances in Combinatorics
PY  - 2023
UR  - http://geodesic.mathdoc.fr/item/ADVC_2023_a0/
LA  - en
ID  - ADVC_2023_a0
ER  - 
%0 Journal Article
%A Matt DeVos
%A Daryl Funk
%A Luis Goddyn
%A Gordon Royle
%T There are only a finite number of excluded minors for the class of bicircular matroids
%J Advances in Combinatorics
%D 2023
%U http://geodesic.mathdoc.fr/item/ADVC_2023_a0/
%G en
%F ADVC_2023_a0
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 Combinatorics (2023). http://geodesic.mathdoc.fr/item/ADVC_2023_a0/