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

Two more proofs that the Kinoshita graph is knotted