Conway-Gordon type theorem for the complete four-partite graph $K_{3,3,1,1}$

Abstract

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.

21 pages, 11 figures

References in corpus (1)

• On intrinsically knotted or completely 3-linked graphs