Many empty triangles have a common edge

Imre Bárány, Jean-François Marckert, Matthias Reitzner

Given a finite point set $X$ in the plane, the degree of a pair $\{x,y\}\subset X$ is the number of empty triangles $t=conv\{x,y,z\}$, where empty means $t\cap X=\{x,y,z\}$. Defin…