On a Planarity Criterion Coming from Knot Theory
| dc.creator | Sawollek, J. | |
| dc.date | 2000-01-25 | |
| dc.date | 2002-08-29 | |
| dc.date.accessioned | 2026-07-07T04:33:25Z | |
| dc.date.available | 2026-07-07T04:33:25Z | |
| dc.description | A graph G is called "minimalizable" if a diagram with minimal crossing number can be obtained from an arbitrary diagram of G by crossing changes. If, furthermore, the minimal diagram is unique up to crossing changes then G is called "strongly minimalizable". In this article, it is explained how minimalizability of a graph is related to its automorphism group and it is shown that a graph is strongly minimalizable if the automorphism group is trivial or isomorphic to a product of symmetric groups. Then, the treatment of crossing number problems in graph theory by knot theoretical means is discussed and, as an example, a planarity criterion for minimalizable graphs is given. | |
| dc.description | 14 pages, 9 figures, latex2e, metafont; Theorems 1 and 7 modified, example and lemma 11 added; definition clarified and minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0001140 | |
| dc.identifier | http://arxiv.org/abs/math/0001140 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58570 | |
| dc.subject | Geometric Topology | |
| dc.subject | Combinatorics | |
| dc.subject | 05C10; 57M15 | |
| dc.title | On a Planarity Criterion Coming from Knot Theory | |
| dc.type | text |