結び目の円周数による特徴付け
スポンサーリンク
概要
- 論文の詳細を見る
A spatial embedding of a graph G is a realization of G into the 3-dimensional Euclidean space R^3. J. H. Conway and C. McA. Gordon proved that every spatial embedding of the complete graph with 7 vertices contains a nontrivial knot. A linear spatial embedding of a graph into R^3 is an embedding which maps each edge to a single straight line segment. In this paper, we actually construct a linear spatial embedding of the complete graph with 2n — 1 (or 2n) vertices which contains the torus knot T(2n — 5, 2) (n ≧ 4). A circular spatial embedding of a graph into R^3 is an embedding which maps each edge to a round arc. We define the circular number of a knot as the minimal number of round arcs in R^3 among such embeddings of the knot. Then we have relations between a circular number and other invariants. We also show that a knot has circular number 3 if and only if the knot is a trefoil knot, and the figure-eight knot has circular number 4.
- 近畿大学理工学部の論文
近畿大学理工学部 | 論文
- 重相関分析のためのプログラム開発と我国自動車産業への応用について
- 交差点付近における聴覚障害者の視覚情報の特徴
- Hamilton C_k-foil designs
- 軸部を細くした高力ボルトの引張り耐力について
- Synthesis of a class of two-variable positive real functions