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- W4308609534 abstract "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." @default.
- W4308609534 created "2022-11-13" @default.
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- W4308609534 date "2021-02-04" @default.
- W4308609534 modified "2023-09-23" @default.
- W4308609534 title "There are only a finite number of excluded minors for the class of bicircular matroids" @default.
- W4308609534 doi "https://doi.org/10.48550/arxiv.2102.02929" @default.
- W4308609534 hasPublicationYear "2021" @default.
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