A property of trivalent graphs related to equidissections
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arXiv
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| Format: | Preprint |
| Published: |
2014
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| _version_ | 1866912380093464576 |
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| author | Rudenko, Daniil |
| author_facet | Rudenko, Daniil |
| contents | Monsky proved that a square cannot be dissected into an odd number of triangles of equal area. Stein conjectured that the same holds for any polygon whose edges can be paired into parallel and equal-length segments. We prove Stein's conjecture under an assumption that all triangle vertices have rational coordinates. Our result is derived from a more general property of trivalent graphs equipped with a $\mathbb{Q}^2$-valued flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1411_0285 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | A property of trivalent graphs related to equidissections Rudenko, Daniil Combinatorics 52C20 (Primary) 52C20 (Secondary) Monsky proved that a square cannot be dissected into an odd number of triangles of equal area. Stein conjectured that the same holds for any polygon whose edges can be paired into parallel and equal-length segments. We prove Stein's conjecture under an assumption that all triangle vertices have rational coordinates. Our result is derived from a more general property of trivalent graphs equipped with a $\mathbb{Q}^2$-valued flow. |
| title | A property of trivalent graphs related to equidissections |
| topic | Combinatorics 52C20 (Primary) 52C20 (Secondary) |
| url | https://arxiv.org/abs/1411.0285 |