cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A384639 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 (that is, no proper subset of the embedding separates the genus n surface).

Original entry on oeis.org

1, 5, 26, 217, 3555, 118993
Offset: 0

Views

Author

J. J. P. Veerman, Aug 13 2025

Keywords

Examples

			For genus 0: only the circle.
For genus 1: 1 circle, 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. A387066, A387067, A387068.

A387067 Number of equivalence classes (up to graph homeomorphism) of finite,connected 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.

Original entry on oeis.org

1, 3, 17, 164, 3096, 111445
Offset: 0

Views

Author

J. J. P. Veerman, Aug 15 2025

Keywords

Comments

n is called the minimal separating genus.

Examples

			For genus 0: only the circle.
For genus 1: 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, A387068.

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.

Original entry on oeis.org

1, 3, 31, 1831, 462638, 243066565
Offset: 0

Views

Author

J. J. P. Veerman, Aug 15 2025

Keywords

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.
Showing 1-3 of 3 results.

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