A387068 Number of equivalence classes (up to homeomorphism) of finite, connected ribbon graphs that have an embedding in an orientable surface of genus n which minimally separates the surface of genus n (that is, no proper subset of the embedding separates the genus n surface) but not the surface of genus n-1.

1, 3, 31, 1831, 462638, 243066565

Offset: 0

Author

J. J. P. Veerman, Aug 15 2025

Keywords

• nonn
• more

Comments

n is called the least separating genus.

These numbers are larger than those of A387067, because different embeddings of the same graph are counted separately. For instance, there is a ribbon graph for the bouquet of 3 circles with least separating genus 1 and a different embedding with least separating genus 2.

Examples

			For genus 0: thickened circle.
For genus 1: thickened versions of a bouquet of 2 circles, bouquet of 3 circles, 4-fold multi-edge.
		

References

• C. N. Aagaard and J. J. P. Veerman, Classification of Minimal Separating Sets of Low Genus Surfaces, Topology and its Applications, Accepted, 2025.

Crossrefs

Cf. A384639, A387066, A387067.