Logarithmic basis number of graphs

Lineage and corrections

VibeMathed record: Logarithmic basis number of graphs evidence for this event

This event attributed to ChatGPT-5.6 Sol

Logarithmic basis number of graphs parent of this event

Miraftab, Morin and Yuditsky, who state it as Conjecture 12 evidence for this event

This event attributed to Kolja Knauer

Logarithmic basis number of graphs evidence for this event

Knauer proves that every finite $n$-vertex multigraph satisfies $\mathrm{bn}(G)=O(\log n)$, improving the previous general $O(\log^2 n)$ bound and matching the known $\Omega(\log n)$ order. He also proves the sharper cycle-rank bound $\mathrm{bn}(G)=O(\log\beta(G))$. Combined with a reduction of Lehner and Miraftab, this yields $\mathrm{bn}(G)=O(\log g)$ for graphs of Euler genus $g$, improving the previous $O(\log^2 g)$ bound to the optimal logarithmic order. parent of this event

Bazargani, Biedl, Bose, Maheshwari and Miraftab, where the question is asked (Section 5) evidence for this event