A new intrinsically knotted graph with 22 edges
| Autor: | Hwa Jeong Lee, Thomas W. Mattman, Minjung Lee, Hyoungjun Kim, Seungsang Oh |
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| Rok vydání: | 2017 |
| Předmět: |
Spatial graph
010102 general mathematics Geometric Topology (math.GT) 0102 computer and information sciences Mathematics::Geometric Topology 01 natural sciences Graph Vertex (geometry) Combinatorics Mathematics - Geometric Topology 010201 computation theory & mathematics FOS: Mathematics Embedding Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 228:303-317 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2017.06.013 |
| Popis: | A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell, and Michael showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh (and, independently, Barsotti and Mattman) proved there are exactly 14 intrinsically knotted graphs with 21 edges by showing that H 12 and C 14 are the only triangle-free intrinsically knotted graphs of size 21. Our current goal is to find the complete set of intrinsically knotted graphs with 22 edges. To this end, using the main argument in [9] , we seek triangle-free intrinsically knotted graphs. In this paper we present a new intrinsically knotted graph with 22 edges, called M 11 . We also show that there are exactly three triangle-free intrinsically knotted graphs of size 22 among graphs having at least two vertices with degree 5: cousins 94 and 110 of the E 9 + e family, and M 11 . Furthermore, there is no triangle-free intrinsically knotted graph with 22 edges that has a vertex with degree larger than 5. |
| Databáze: | OpenAIRE |
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