Title: Koszul binomial edge ideals of pairs of graphs,
Abstract: We study the Koszul property of a standard graded $K$-algebra $R$ defined by
the binomial edge ideal of a pair of graphs $(G_1,G_2)$. We show that the
following statements are equivalent: (i) $R$ is Koszul; (ii) the defining ideal
$J_{G_1,G_2}$ of $R$ has a quadratic Gröbner basis; (iii) the graded maximal
ideal of $R$ has linear quotients with respect to a suitable order of its
generators