Conway-Gordon type theorem for the complete four-partite graph   $K_{3,3,1,1}$
  We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph $K_{3,3,1,1}$ in terms of the square of the linking number and the second coefficient of the Conway polynomial. As an application, we show that every rectilinear spatial $K_{3,3,1,1}$ contains a nontrivial Hamiltonian knot. 
Hiroka Hashimoto, Ryo Nikkuni
math.GT