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Bipartite Intrinsically Knotted Graphs with 22 Edges
- Title
- Bipartite Intrinsically Knotted Graphs with 22 Edges
- Authors
- Kim, Hyoungjun; Mattman, Thomas; Oh, Seungsang
- Ewha Authors
- 김형준
- SCOPUS Author ID
- 김형준
- Issue Date
- 2017
- Journal Title
- JOURNAL OF GRAPH THEORY
- ISSN
- 0364-9024
1097-0118
- Citation
- JOURNAL OF GRAPH THEORY vol. 85, no. 2, pp. 568 - 584
- Keywords
- 2010 Mathematics Subject Classification: 57M25; 57M27; 05C10
- Publisher
- WILEY
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- A graph is intrinsically knotted if every embedding contains a nontrivially knotted cycle. It is known that intrinsically knotted graphs have at least 21 edges and that the KS graphs, K-7 and the 13 graphs obtained from K-7 by del Y moves, are the only minor minimal intrinsically knotted graphs with 21 edges [1, 9, 11, 12]. This set includes exactly one bipartite graph, the Heawood graph. In this article we classify the intrinsically knotted bipartite graphs with at most 22 edges. Previously known examples of intrinsically knotted graphs of size 22 were those with KS graph minor and the 168 graphs in the K-3,K-3,K-1,K-1 and E-9 + e families. Among these, the only bipartite example with no Heawood subgraph is Cousin 110 of the E-9 + e family. We show that, in fact, this is a complete listing. That is, there are exactly two graphs of size at most 22 that are minor minimal bipartite intrinsically knotted: the Heawood graph and Cousin 110. (C) 2016 Wiley Periodicals, Inc.
- DOI
- 10.1002/jgt.22091
- Appears in Collections:
- 연구기관 > 수리과학연구소 > Journal papers
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