arXiv subjects

Hiroka Hashimoto

Publications and source records attributed to Hiroka Hashimoto.

2 recordsLinked to original sources

arXiv2012

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.

math.GT↗

arXiv2012

On Conway-Gordon type theorems for graphs in the Petersen family

For every spatial embedding of each graph in the Petersen family, it is known that the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2. In this paper, we give an integral lift of this formula in terms of the square of the linking number and the second coefficient of the Conway polynomial.

math.GT↗