Knots in the canonical book representation of complete graphs
| Autor: | Dana Rowland, Andrea Politano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Conjecture
Mathematics::Combinatorics Coprime integers General Mathematics Complete graph Geometric Topology (math.GT) spatial graph Hamiltonian path Mathematics::Geometric Topology Torus knot Combinatorics symbols.namesake Mathematics - Geometric Topology Knot (unit) intrinsically knotted 57M15 canonical book 57M25 symbols FOS: Mathematics Embedding Mathematics 05C10 |
| Zdroj: | Involve 6, no. 1 (2013), 65-81 |
| Popis: | We describe which knots can be obtained as cycles in the canonical book representation of K_n, the complete graph on n vertices. We show that the canonical book representation of K_n contains a Hamiltonian cycle that is a composite knot if and only if n>11 and we show that when p and q are relatively prime, the (p,q) torus knot is a Hamiltonian cycle in the canonical book representation of K_{2p+q}. Finally, we list the number and type of all non-trivial knots that occur as cycles in the canonical book representation of K_n for n 17 pages, 9 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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