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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.17624 |
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| _version_ | 1866914277808406528 |
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| author | McGuinness, Sean |
| author_facet | McGuinness, Sean |
| contents | DeVos et al conjectured that if $M$ is a simple, regular matroid and $c$ is a colouring of the elements of $M$ with $r(M)+1$ colours, where each colour class has at least two elements, then $M$ contains a rainbow circuit of size at most $\lceil \frac {r(M)+1}2 \rceil.$ We prove this conjecture by showing that for all such regular matroids there are four rainbow circuits $C_i,\ i = 1,2,3,4$ for which $\sum_i |C_i| \le 2r(M) +4$ and for which no element of $M$ belongs to more than two of the circuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17624 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Short Rainbow Circuits in Regular Matroids McGuinness, Sean Combinatorics DeVos et al conjectured that if $M$ is a simple, regular matroid and $c$ is a colouring of the elements of $M$ with $r(M)+1$ colours, where each colour class has at least two elements, then $M$ contains a rainbow circuit of size at most $\lceil \frac {r(M)+1}2 \rceil.$ We prove this conjecture by showing that for all such regular matroids there are four rainbow circuits $C_i,\ i = 1,2,3,4$ for which $\sum_i |C_i| \le 2r(M) +4$ and for which no element of $M$ belongs to more than two of the circuits. |
| title | Short Rainbow Circuits in Regular Matroids |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2601.17624 |