Projective plane graphs and 3-rigidity
Combinatorics
2023-02-20 v2
Abstract
It is shown that a simple graph which is embeddable in the real projective plane is minimally 3-rigid if and only if it is (3,6)-tight. Moreover the topologically uncontractible embedded graphs of this type are constructible from one of 8 embedded graphs by a sequence of vertex splitting moves. In particular the characterisation of minimal 3-rigidity holds for a triangulated Mobius strip.
Cite
@article{arxiv.2003.05514,
title = {Projective plane graphs and 3-rigidity},
author = {Eleftherios Kastis and Stephen Power},
journal= {arXiv preprint arXiv:2003.05514},
year = {2023}
}
Comments
34 pages (including a 9 page appendix). This is a substantial revision with fuller details and improved terminology. The main results are unchanged but there are new proofs and diagrams