Bibliographic Information
- Other Title
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- 結び目の円周数による特徴付け
- ムスビメ ノ エンシュウスウ ニ ヨル トクチョウズケ
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Abstract
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.
Departmental Bulletin Paper
application/pdf
Journal
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- Journal of the Faculty of Science and Engineering, Kinki University
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Journal of the Faculty of Science and Engineering, Kinki University (44), 1-4, 2008-09-01
近畿大学理工学部
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Keywords
Details 詳細情報について
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- CRID
- 1050282677521858432
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- NII Article ID
- 120005736176
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- NII Book ID
- AN00064168
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- ISSN
- 03864928
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- NDL BIB ID
- 9720916
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- Text Lang
- ja
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- Article Type
- departmental bulletin paper
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- Data Source
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- IRDB
- NDL
- CiNii Articles