The width of the perfect matching graph for knots
A knot is a circle embedded in three-space, but we immediately translate it into a bipartite graph Gamma following previous work of the author. We consider the graph G of perfect matchings of this graph Gamma, providing a combinatorial formula for the width of G. We present several properties of Gamma and construct a partition of its vertices into cycles that relate directly to G.
This work was inspired by a seminar talk by Roy Ben-Ari on part of his Masters thesis under the supervision of Ron Adin and Yuval Roichman.
This is joint work with Mina Teicher.