Exactly fourteen intrinsically knotted graphs have 21 edges
Min Jung Lee, Hyoung Jun Kim, Hwa Jeong Lee, and Seungsang Oh
TL;DR
This paper proves that exactly fourteen graphs with 21 edges are intrinsically knotted, confirming that no other such graphs exist beyond the known 14, including K7 and its rY move variants.
Contribution
It establishes the uniqueness of the 14 intrinsically knotted graphs with 21 edges, completing the classification.
Findings
Exactly 14 intrinsically knotted graphs have 21 edges
K7 and its rY move variants are among these graphs
No other graphs with 21 edges are intrinsically knotted
Abstract
Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Also it is known that K7 and the thirteen graphs obtained from K7 by rY moves are intrinsically knotted graphs with 21 edges. We prove that these 14 graphs are the only intrinsically knotted graphs with 21 edges.
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Taxonomy
TopicsArtificial Intelligence in Games · Computational Geometry and Mesh Generation · Digital Games and Media