Flexible placements of periodic graphs in the plane
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2019
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909083167096832 |
|---|---|
| author | Dewar, Sean |
| author_facet | Dewar, Sean |
| contents | Given a periodic graph, we wish to determine via combinatorial methods whether it has periodic embeddings in the plane that -- via motions that preserve edge-lengths and periodicity -- can be continuously deformed into another non-congruent embedding of the graph. By introducing NBAC-colourings for the corresponding quotient gain graphs, we identify which periodic graphs have flexible embeddings in the plane when the lattice of periodicity is fixed. We further characterise with NBAC-colourings which 1-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity, and characterise in special cases which 2-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1911_05634 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Flexible placements of periodic graphs in the plane Dewar, Sean Combinatorics Metric Geometry 52C25, 13A18 Given a periodic graph, we wish to determine via combinatorial methods whether it has periodic embeddings in the plane that -- via motions that preserve edge-lengths and periodicity -- can be continuously deformed into another non-congruent embedding of the graph. By introducing NBAC-colourings for the corresponding quotient gain graphs, we identify which periodic graphs have flexible embeddings in the plane when the lattice of periodicity is fixed. We further characterise with NBAC-colourings which 1-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity, and characterise in special cases which 2-periodic graphs have flexible embeddings in the plane with a flexible lattice of periodicity. |
| title | Flexible placements of periodic graphs in the plane |
| topic | Combinatorics Metric Geometry 52C25, 13A18 |
| url | https://arxiv.org/abs/1911.05634 |