2 problems

Let $G$ be an $n$-vertex graph, and let $\operatorname{bn}(G)$ denote the basis number of $G$. Biedl's logarithmic basis number conjecture. Every $n$-vertex graph $G$ has … The con…

Let $G$ be a graph, let $k$ be a nonnegative integer, and let $\operatorname{bn}(G)$ denote the basis number of $G$. Treewidth-linear basis number conjecture. Every graph $G$ of tr…