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KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K-7 INTO R-3
- Authors
- Huh, Youngsik
- Issue Date
- Dec-2012
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Keywords
- Polygonal knot; figure-8 knot; complete graph; linear embedding
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.21, no.14, pp.1 - 14
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- Volume
- 21
- Number
- 14
- Start Page
- 1
- End Page
- 14
- ISSN
- 0218-2165
- Abstract
- In 1983 Conway and Gordon proved that any embedding of the complete graph K-7 into R-3 contains at least one nontrivial knot as its Hamiltonian cycle. After their work knots (also links) are considered as intrinsic properties of abstract graphs, and numerous subsequent works have been continued until recently. In this paper, we are interested in knotted Hamiltonian cycles in linear embedding of K-7. Concretely it is shown that any linear embedding of K-7 contains at most three figure-8 knots.
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Related Researcher
- Huh, Young sik
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)