Volume 15, issue 6 (2015)

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Exactly fourteen intrinsically knotted graphs have $21$ edges

Minjung Lee, Hyoungjun Kim, Hwa Jeong Lee and Seungsang Oh

Algebraic & Geometric Topology 15 (2015) 3305–3322
Abstract

Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least $21$ edges. Also it is known that ${K}_{7}$ and the thirteen graphs obtained from ${K}_{7}$ by $\nabla Y$ moves are intrinsically knotted graphs with $21$ edges. We prove that these 14 graphs are the only intrinsically knotted graphs with $21$ edges.

Keywords
intrinsically knotted, graph
Mathematical Subject Classification 2010
Primary: 57M25, 57M27