Intrinsically knotted graphs with 21 edges

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We show that the 14 graphs obtained by moves on K₇ constitute a complete list of the minor minimal intrinsically knotted graphs on 21 edges. We also present evidence in support of a conjecture that the 20 graph Heawood family, obtained by a combination of and Y∇ moves on K₇, is the list of graphs of size 21 that are minor minimal with respect to the property not 2--apex.