A387066 Number of equivalence classes (up to graph homeomorphism) of finite 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, 4, 21, 191, 3338, 115438

Offset: 0

Author

J. J. P. Veerman, Aug 15 2025

Keywords

• nonn
• more

Comments

n is called the least separating genus.

Examples

			For genus 0: only the circle.
For genus 1: 2 circles, 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.
• J. Bernhard and J. J. P. Veerman, The Topology of Surface Mediatrices, Topology and its Applications, 154, 54-68, 2007.

Crossrefs

Cf. A384639, A387067, A387068.