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Intrinsically knotted graphs with 21 edges

Abstract

We show that the 14 graphs obtained by βˆ‡Y\nabla\mathrm{Y} moves on K_7 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 βˆ‡Y\nabla\mathrm{Y} and Yβˆ‡\mathrm{Y}\nabla moves on K_7, is the list of graphs of size 21 that are minor minimal with respect to the property not 2--apex.Comment: 21 pages, 11 figure

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