2 papers
math.GT2008★ 9 cited
On the Harary-Kauffman Conjecture and Turk's Head Knots
Nicholas E. Dowdall, Thomas W. Mattman, Kevin Meek +1
The m,n Turk's Head Knot, THK(m,n), is an "alternating (m,n) torus knot." We prove the Harary-Kauffman conjecture for all THK(m,n) except for the case where m \geq 5 is odd and n \…
math.GT2008★ 2 cited
A sufficient condition for intrinsic knotting of bipartite graphs
Sophy Huck, Alexandra Appel, Miguel-Angel Manrique +1
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…