Abstract
We show that the 20-graph Heawood family, obtained by a combination of and moves on , is precisely the set of graphs of at most 21 edges that are minor-minimal with respect to the property “not -apex”. As a corollary, this gives a new proof that the 14 graphs obtained by moves on are the minor-minimal intrinsically knotted graphs of 21 or fewer edges. Similarly, we argue that the seven-graph Petersen family, obtained from , is the set of graphs of at most 17 edges that are minor-minimal with respect to the property “not apex”.
Citation
Jamison Barsotti. Thomas W. Mattman. "Graphs on 21 edges that are not 2-apex." Involve 9 (4) 591 - 621, 2016. https://doi.org/10.2140/involve.2016.9.591
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