A sufficient condition for intrinsic knotting of bipartite graphs
Geometric Topology
2008-11-04 v1
Abstract
We present evidence in support of a conjecture that a bipartite graph with at least five vertices in each part and |E(G)| \geq 4 |V(G)| - 17 is intrinsically knotted. We prove the conjecture for graphs that have exactly five or exactly six vertices in one part. We also show that there is a constant C_n such that a bipartite graph with exactly n \geq 5 vertices in one part and |E(G)| \geq 4 |V(G)| + C_n is intrinsically knotted. Finally, we classify bipartite graphs with ten or fewer vertices with respect to intrinsic knotting.
Keywords
Cite
@article{arxiv.0811.0036,
title = {A sufficient condition for intrinsic knotting of bipartite graphs},
author = {Sophy Huck and Alexandra Appel and Miguel-Angel Manrique and Thomas W Mattman},
journal= {arXiv preprint arXiv:0811.0036},
year = {2008}
}
Comments
10 pages, 1 figure