2024/05/29 by Sutanoya Chakraborty, Arijit Ghosh, Chakraborty, Sutanoya +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2405.19274
openalex publication_date 2024/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a drawing D of a graph G, we define the crossing number between any two cycles C1 and C2 in D to be the number of crossings that involve at least one edge from each of C1 and C2 except the crossings between edges that are common to both cycles. We show that if the crossing number between every two cycles in G is even in a drawing of G on the plane, then there is a planar drawing of G. This result can be extended to arbitrary surfaces. We also establish an equivalence between our result and a fundamental result due to Cairns-Nikolayevsky and Pelsmajer-Schaefer-Štefankovič, about drawing graphs on surfaces, and derive the Loebl-Masbaum theorem from it.