Two more proofs that the Kinoshita graph is knotted

Abstract

The Kinoshita graph is a particular embedding in the 3-sphere of a graph with three edges, two vertices and no loops. It has the remarkable property that although the removal of any edge results in an unknotted loop, the Kinoshita graph is itself knotted. We use two classical theorems from knot theory to give two particularly simple proofs that the Kinoshita graph is knotted. Apart from appealing to the two classical theorems, the exposition is elementary and is aimed at those with only a passing familiarity with knot theory.