Dips at small sizes for topological graph obstruction sets
Abstract
The Graph Minor Theorem of Robertson and Seymour implies a finite set of obstructions for any minor closed graph property. We show that there are only three obstructions to knotless embedding of size 23, which is far fewer than the 92 of size 22 and the hundreds known to exist at larger sizes. We describe several other topological properties whose obstruction set demonstrates a similar dip at small size. For order ten graphs, we classify the 35 obstructions to knotless embedding and the 49 maximal knotless graphs.
Keywords
Cite
@article{arxiv.2205.14255,
title = {Dips at small sizes for topological graph obstruction sets},
author = {Hyoungjun Kim and Thomas W. Mattman},
journal= {arXiv preprint arXiv:2205.14255},
year = {2024}
}
Comments
v2 42 pages, 17 figures, 3 tables; Substantial revisions. Proof of IK for G_1 and G_2 moved to Appendix A. Classification of maximal knotless graphs of order ten added as Appendix B. Appendix C included with graph6 format of most graphs referenced. For Appendix C see http://tmattman.yourweb.csuchico.edu/Appendix.txt