The Heawood families are significant in topological graph theory.
The family consists of 20 graphs, all of which have 21 edges.
The unique largest member, the Heawood graph, has 14 vertices.
[1] Only 14 out of the 20 graphs are intrinsically knotted, all of which are minor minimal with this property.
[1] This shows that knotless graphs are not closed under ΔY- and YΔ-transformations.
-family is generated from the complete multipartite graph
The family consists of 58 graphs, all of which have 22 edges.
The unique largest member has 14 vertices.
[1] All graphs in this family are intrinsically knotted and are minor minimal with this property.
through repeated application of ΔY- and YΔ-transformations is the disjoint union of the
Hein van der Holst (2006) showed that the graphs in the Heawood family are not 4-flat and have Colin de Verdière graph invariant
Van der Holst suggested that they might form the complete list of excluded minors for both the 4-flat graphs and the graphs with
[2] This conjecture can be further motivated from structural similarities to other topologically defined graphs classes: