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Family sizes
for complete multipartite graphs
Danielle Gregg, Thomas W. Mattman, Zachary Porat and George Todd
Vol. 15 (2022), No. 4, 669–686
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Abstract |
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The obstruction set for graphs with knotless embeddings is not known, but a recent paper of Goldberg, Mattman, and Naimi indicates that it is quite large. Almost all known obstructions fall into four triangle-Y families and they ask if there is an efficient way of finding or estimating the size of such graph families. Inspired by this question, we investigate the family size for complete multipartite graphs. Aside from three families that appear to grow exponentially, these families stabilize: after a certain point, increasing the number of vertices in a fixed part does not change family size. |
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Keywords
spatial graphs, intrinsic knotting
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Mathematical Subject Classification
Primary: 05C10
Secondary: 05C35, 57M15
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Milestones
Received: 2 September 2021
Revised: 21 December 2021
Accepted: 31 December 2021
Published: 7 January 2023
Communicated by Joel Foisy
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Authors |
| Danielle Gregg | |
| Department of Mathematics Union College Schenectady, NY United States |
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| Thomas W. Mattman | |
| Department of Mathematics and
Statistics California State University Chico, CA United States |
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| Zachary Porat | |
| Department of Mathematics and
Computer Science Wesleyan University Middletown, CT United States |
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| George Todd | |
| Department of Mathematics University of Dayton Dayton, OH United States |
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