The enhanced conflict graph extreme-point conjecture for 2×N switches

Consider a $2\times N$ switch with traffic consisting of unicasts and broadcasts, and let $G$ be its enhanced conflict graph. Let $QSTAB(G)$ denote the fractional stable set polytope, and let $STAB(G)$ denote the stable set polytope. The stable sets of $G$ and the points $\boldsymbol{v}(m,U,V)$ described in Theorem 2 are known extreme points of $QSTAB(G)$. The enhanced conflict graph extreme-point conjecture. $QSTAB(G)$ has no other extreme points besides the stable sets and the points $\boldsymbol{v}(m,U,V)$. If true, the stated bound on the fractional weighted chromatic number would imply that an expansion factor of $1.25$ suffices for every vertex of $QSTAB(G)$ in the $2\times N$ case. This remains a conjecture in the paper; simulations motivate extending the approach to $K\times N$ switches.