Conway-Gordon type theorem for the complete four-partite graph K3,3,1,1
Abstract
We give a Conway-Gordon type formula for invariants of knots and links in a spatial complete four-partite graph K3,3,1,1 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 K3,3,1,1 contains a nontrivial Hamiltonian knot.
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