2000/01/25 by Jörg Sawollek, J. Sawollek, Sawollek, J.
Computer Science · Mathematics · #05C10 #57M15 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CO #math.GT #msc:05C10 #msc:57M15
paper · pdf · doi:10.48550/arxiv.math/0001140
14 pages, 9 figures, latex2e, metafont; Theorems 1 and 7 modified, example and lemma 11 added; definition clarified and minor corrections
openalex publication_date 2000/01/25 · arxiv created 2002/08/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.