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pro vyhledávání: '"Daryl Funk"'
Let $M$ be a representable matroid on $n$ elements. We give bounds, in terms of $n$, on the least positive characteristic and smallest field over which $M$ is representable.
18 pages
18 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a20c3dabfaf2d0fc7d45184aab969fb0
We conjecture that the class of frame matroids can be characterised by a sentence in the monadic second-order logic of matroids, and we prove that there is such a characterisation for the class of bicircular matroids. The proof does not depend on an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2b74bb067de1ca5656b4e0ed36b5c133
http://arxiv.org/abs/2005.04526
http://arxiv.org/abs/2005.04526
Autor:
Daryl Funk, Dillon Mayhew
Publikováno v:
Discrete Mathematics. 341:1509-1522
Frame matroids and lifted-graphic matroids are two distinct minor-closed classes of matroids, each of which generalises the class of graphic matroids. The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, simultane
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f7bea3b6944cc6065bf93c8a0c5af6f
https://doi.org/10.1016/j.disc.2018.02.022
https://doi.org/10.1016/j.disc.2018.02.022
Hlineny's Theorem shows that any sentence in the monadic second-order logic of matroids can be tested in polynomial time, when the input is limited to a class of F-representable matroids with bounded branch-width (where F is a finite field). If each
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e063641f6c93ff3965a55fb652a19ba6
http://arxiv.org/abs/1910.04360
http://arxiv.org/abs/1910.04360
Publikováno v:
European Journal of Combinatorics. 85:103062
The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and lifted-graphic matroids introduced earlier by Zaslavsky. For each biased graph ( G , B ) Zaslavsky defined a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9a6fd64f3107d0fbdd5105b83aeaaae4
https://doi.org/10.1016/j.ejc.2019.103062
https://doi.org/10.1016/j.ejc.2019.103062
Autor:
Sebastián González Hermosillo de la Maza, Daryl Funk, Bojan Mohar, Amanda Montejano, Matthew Drescher, Krystal Guo, Tony Huynh, Matt DeVos
Let $G$ be a simple $n$-vertex graph and $c$ be a colouring of $E(G)$ with $n$ colours, where each colour class has size at least $2$. We prove that $(G,c)$ contains a rainbow cycle of length at most $\lceil \frac{n}{2} \rceil$, which is best possibl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f85a8edfca973961009377df4101d8f0
We give upper and lower bounds on the number of delta-matroids, and on the number of even delta-matroids.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f446a619a076126dfd7b94631296d33c
https://eprints.bbk.ac.uk/id/eprint/20523/1/Delta_matroids170321.pdf
https://eprints.bbk.ac.uk/id/eprint/20523/1/Delta_matroids170321.pdf
Autor:
Matt DeVos, Daryl Funk
Given a 3-connected biased graph Ω with a balancing vertex, and with frame matroid F ( Ω ) nongraphic and 3-connected, we determine all biased graphs Ω ′ with F ( Ω ′ ) = F ( Ω ) . As a consequence, we show that if M is a 4-connected nongrap
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7eb71268a1912d6b272d37299d7f898e
http://arxiv.org/abs/1606.07370
http://arxiv.org/abs/1606.07370
Autor:
Daryl Funk, Richard C. Brewster
Publikováno v:
Journal of Graph Theory. 71:182-191
The topological approach to the study of infinite graphs of Diestel and KUhn has enabled several results on Hamilton cycles in finite graphs to be extended to locally finite graphs. We consider the result that the line graph of a finite 4-edge-connec
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8d7d9a7227ff6a712370cab96d0c31d5
https://doi.org/10.1002/jgt.20641
https://doi.org/10.1002/jgt.20641
We investigate the set of excluded minors of connectivity 2 for the class of frame matroids. We exhibit a list $\mathcal{E}$ of 18 such matroids, and show that if $N$ is such an excluded minor, then either $N \in \mathcal{E}$ or $N$ is a 2-sum of $U_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1b9f53e2bff350e62df6e78af23d7fd