2015/11/16 by Dawei He, Yan Wang, He, Dawei +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Collatz conjecture #Combinatorics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Computer graphics (images) #Computer science #Conjecture #Discrete mathematics #FOS: Mathematics #Graph #History #Mathematics #Order (exchange) #Planar #Planar graph #Subdivision #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1511.05020
published in arXiv (Cornell University) (Cornell University)
arxiv created 2015/11/16 · openalex publication_date 2015/11/16 · arxiv updated 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of K5. This conjecture was proved by Ma and Yu for graphs containing K4-, and an important step in their proof is to deal with a 5-separation in the graph with a planar side. In order to establish the Kelmans-Seymour conjecture for all graphs, we need to consider 5-separations and 6-separations with less restrictive structures. The goal of this paper is to deal with special 5-separations and 6-separations, including those with an apex side. Results will be used in subsequent papers to prove the Kelmans-Seymour conjecture.