Author

Kolja B. Knauer

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Preprint Sep 2026

Merino-Welsh inequalities for matroids with controlled lattices of cyclic flats

Beke, Cs\'aji, Csikv\'ari, and Pituk showed that the Merino--Welsh quotient $\Phi(M)=T_M(1,1)^2/(T_M(2,0)T_M(0,2))$ can be arbitrarily large, so the multiplicative Merino-Welsh inequality fails for matroids in general. We show that $\Phi$ is uniformly bounded on the class of matroids whose cyclic-flat lattice avoids an...

Kolja B. Knauer, Leonardo Martínez-Sandoval, C. Merino · 0 citations

Preprint Sep 2026

Rings are $\chi$-bounded

We prove that there is a function $f:\mathbb N\to\mathbb N$ such that $\chi(\Gamma(R))\leq f(\omega(\Gamma(R)))$ for the zero-divisor graph of any ring $R$, if the clique number is finite. On the one hand, this consolidates a disproved conjecture of Beck from 1988, claiming $\chi(\Gamma(R))=\omega(\Gamma(R))$ for unita...

Sara Asensio, Ignacio García-Marco, Kolja B. Knauer · 0 citations

Preprint Sep 2026

Logarithmic basis number of graphs and regular matroids

The basis number $bn(G)$ of a graph $G$ is the minimum edge-congestion of a basis of its cycle space. We prove that every finite $n$-vertex multigraph satisfies $bn(G)=O(\log n)$, resolving, for simple graphs, a question of Bazargani, Biedl, Bose, Maheshwari and Miraftab, subsequently stated as a conjecture by Miraftab...

Kolja B. Knauer · 1 citation