Bipartite intrinsically knotted graphs with 23 edges

Hyoungjun Kim, Thomas Mattman, Seungsang Oh

Research output: Contribution to journalArticlepeer-review


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 there are exactly 14 intrinsically knotted graphs with 21 edges, in which the Heawood graph is the only bipartite graph. The authors showed that there are exactly two graphs with at most 22 edges that are minor minimal bipartite intrinsically knotted: the Heawood graph and Cousin 110 of the E9+e family. In this paper we show that there are exactly six bipartite intrinsically knotted graphs with 23 edges so that every vertex has degree 3 or more. Four among them contain the Heawood graph and the other two contain Cousin 110 of the E9+e family. Consequently, there is no minor minimal intrinsically knotted graph with 23 edges that is bipartite.

Original languageEnglish
Article number113022
JournalDiscrete Mathematics
Issue number11
Publication statusPublished - 2022 Nov


  • Graph embedding
  • Intrinsically knotted

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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