Family sizes for complete multipartite graphs
Combinatorics
2023-01-25 v2
Abstract
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.
Cite
@article{arxiv.2008.12975,
title = {Family sizes for complete multipartite graphs},
author = {Danielle Gregg and Thomas W. Mattman and Zachary Porat and George Todd},
journal= {arXiv preprint arXiv:2008.12975},
year = {2023}
}
Comments
15 pages, 6 figures, 8 tables v2 - substantial revision including improved estimate of family size of K_n family