论文标题
随机gf（q） - 代表性的矩形不是（b，c） - 可拆卸
Random GF(q)-representable matroids are not (b,c)-decomposable
论文作者
论文摘要
We show that a random subset of the rank-$n$ projective geometry $\text{PG}(n-1,q)$ is, with high probability, not $(b,c)$-decomposable: if $k$ is its colouring number, it does not admit a partition of its ground set into classes of size at most $ck$, every transversal of which is $b$-colourable.这是Abdolazimi，Karlin，Klein和Oveis Gharan（Arxiv：2111.12436）的最新结果以及Leichter，Moseley和Pruhs（Arxiv：2206.12896）的结果，他们显示了$ \ text {pg}（pg}（n-1，q）不是$（n-1，q）$（$（1）$（1，c）。而不是$（b，c）$ - 可分解。
We show that a random subset of the rank-$n$ projective geometry $\text{PG}(n-1,q)$ is, with high probability, not $(b,c)$-decomposable: if $k$ is its colouring number, it does not admit a partition of its ground set into classes of size at most $ck$, every transversal of which is $b$-colourable. This generalises recent results by Abdolazimi, Karlin, Klein, and Oveis Gharan (arXiv:2111.12436) and by Leichter, Moseley, and Pruhs (arXiv:2206.12896), who showed that $\text{PG}(n-1,q)$ is not $(1,c)$-decomposable, resp. not $(b,c)$-decomposable.
