2 problems

Let $G$ be a weighted triangle-free graph with maximum degree at most $3$; equivalently, $G$ is a weighted triangle-free subcubic graph. Weighted subcubic conjecture. One should ha…

Let $G$ be a weighted triangle-free graph, and let $T$ be a spanning tree of $G$. Spanning-tree bound conjecture. One should have … The conjecture would determine the optimal value…