English

Partial triangulations of surfaces with girth constraints

Geometric Topology 2024-12-10 v4 Combinatorics

Abstract

Barnette and Edelson have shown that there are finitely many minimal triangulations of a connected compact 2-manifold M. Similar finiteness results are obtained for cellular partial triangulations that satisfy various girth inequality constraints for embedded cycles. A characterisation of various M-embedded sparse graphs is given in terms of the satisfaction of higher genus girth inequalities. With this it is shown that there are finitely many contraction-minimal M-embedded graphs that are (3,6)-tight or (3,3)-tight.

Keywords

Cite

@article{arxiv.2309.10638,
  title  = {Partial triangulations of surfaces with girth constraints},
  author = {Stephen C. Power},
  journal= {arXiv preprint arXiv:2309.10638},
  year   = {2024}
}

Comments

Simplified proofs and new results