How to build a pillar: a proof of Thomassen’s conjecture

• Irene Gil Fernández ^[1] ; Hong Liu
  1. [1] University of Warwick

     University of Warwick

     Reino Unido

     
• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 147-152
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Carsten Thomassen in 1989 conjectured that if a graph has minimum degree more thanthe number of atoms in the universe (δ(G) ≥ 101010 ), then it contains a pillar, which isa graph that consists of two vertex-disjoint cycles of the same length, s say, along with svertex-disjoint paths of the same length which connect matching vertices in order around thecycles. Despite the simplicity of the structure of pillars and various developments of powerfulembedding methods for paths and cycles in the past three decades, this innocent lookingconjecture has seen no progress to date. We give a proof of this conjecture by building apillar (algorithmically) in sublinear expanders.