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- W4297130259 abstract "We show that, for each real number $epsilon > 0$ there is an integer $c$ such that, if $M$ is a simple triangle-free binary matroid with $|M| ge (tfrac{1}{4} + epsilon) 2^{r(M)}$, then $M$ has critical number at most $c$. We also give a construction showing that no such result holds for any real number less than $tfrac{1}{4}$. This shows that the critical threshold for the triangle is $tfrac 1 4$. We extend the notion of critical threshold to every simple binary matroid $N$ and conjecture that, if $N$ has critical number $cge 3$, then $N$ has critical threshold $1-icdot 2^{-c}$ for some $iin {2,3,4}$. We give some support for the conjecture by establishing lower bounds." @default.
- W4297130259 created "2022-09-27" @default.
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- W4297130259 date "2014-06-10" @default.
- W4297130259 modified "2023-09-28" @default.
- W4297130259 title "The critical number of dense triangle-free binary matroids" @default.
- W4297130259 doi "https://doi.org/10.48550/arxiv.1406.2588" @default.
- W4297130259 hasPublicationYear "2014" @default.
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