Face Sizes and the Connectivity of the Dual
ABSTRACT For each , we prove tight lower bounds on face sizes that must be present to allow 1‐ or 2‐cuts in simple duals of ‐connected maps. Using these bounds, we determine the smallest genus on which a ‐connected map can have a simple dual with a 2‐cut and give lower and some upper bounds for the smallest genus on which a ‐connected map can have a simple dual with a 1‐cut.
Authors
- Kenta Noguchi (ORCID: https://orcid.org/0000-0002-7790-0782)
- Heidi Van den Camp (ORCID: https://orcid.org/0000-0001-7634-3681)
- Gunnar Brinkmann
Institutions
- HOGENT University of Applied Sciences and Arts (BE)
- Tokyo University of Science (JP)
Publication Details
- Journal
- Journal of Graph Theory
- Published
- 2025-07-13
- DOI
- https://doi.org/10.1002/jgt.23277
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00