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More intrinsically knotted graphs with 22 edges and the restoring method
- Title
- More intrinsically knotted graphs with 22 edges and the restoring method
- Authors
- Kim, Hyoungjun; Mattman, Thomas; Oh, Seungsang
- Ewha Authors
- 김형준
- SCOPUS Author ID
- 김형준
- Issue Date
- 2018
- Journal Title
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS
- ISSN
- 0218-2165
1793-6527
- Citation
- JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS vol. 27, no. 10
- Keywords
- Graph embedding; intrinsically knotted
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman, showed that intrinsically knotted graphs have at least 21 edges. Recently, Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that K-7 and the 13 graphs obtained from K-7 by del Y moves are the only intrinsically knotted graphs with 21 edges. Also Kim, Lee, Lee, Mattman and Oh showed that there are exactly three triangle-free intrinsically knotted graphs with 22 edges having at least two vertices of degree 5. Furthermore, there is no triangle-free intrinsically knotted graph with 22 edges that has a vertex with degree larger than 5. In this paper, we show that there are exactly five triangle-free intrinsically knotted graphs with 22 edges having exactly one degree 5 vertex. These are Cousin 29 of the K-3,K-3,K-1,K-1 family, Cousins 97 and 99 of the E-9 + e family and two others that were previously unknown.
- DOI
- 10.1142/S0218216518500591
- Appears in Collections:
- 연구기관 > 수리과학연구소 > Journal papers
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