5 research outputs found
A new intrinsically knotted graph with 22 edges
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, showed that and the 13
graphs obtained from by moves are the only intrinsically
knotted graphs with 21 edges.
In this paper we present the following results: there are exactly three
triangle-free intrinsically knotted graphs with 22 edges having at least two
vertices of degree 5. Two are the cousins 94 and 110 of the family and
the third is a previously unknown graph named . These graphs are shown
in Figure 3 and 4. Furthermore, there is no triangle-free intrinsically knotted
graph with 22 edges that has a vertex with degree larger than 5