2022/05/12 by Hyoung-Jun Kim, Kim, Hyoungjun, Thomas W. Mattman +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Social Sciences · #05C10 (Primary) 57M15 #57K10 (Secondary) #Artificial Intelligence in Games #Biochemical and Structural Characterization #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Swearing, Euphemism, Multilingualism
paper · pdf · doi:10.48550/arxiv.2205.06199
openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.