2 problems

Let $k$-triangulations be the maximal graphs on $[n]$ with no $(k+1)$-crossing, and let the generic bar-and-joint rigidity matroid of dimension $2k$ be the matroid obtained from ge…

No-common-edge shortest paths conjecture. 1. A shortest path in $G_{n,k}$ between $T$ and $T'$ never flips a common edge of $T$ and $T'$. 2. If $f$ is a $k$-relevant edge of $T$,…