Counting Links and Knots in Complete Graphs
Loren Abrams, Blake Mellor, Lowell Trott
TL;DR
This paper studies the minimal number of links and knots in complete partite graphs, providing exact values and bounds for specific configurations, advancing understanding of topological complexity in graph embeddings.
Contribution
It offers new bounds and exact counts for links and knots in complete partite graphs, including specific cases like K_{4,4,1} and graphs with 8 or 9 vertices.
Findings
Minimal links in K_{4,4,1} is 74
Bounds established for graphs with 8 vertices
Exact values or bounds for all relevant graphs
Abstract
We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Graph theory and applications