Powers of Hamilton cycles in graphs perturbed by a random geometric graph

• Alberto Espuny Díaz ^[1] ; Joseph Hyde ^[2]
  1. [1] Ilmenau University of Technology

     Ilmenau University of Technology

     Ilm-Kreis, Alemania

     
  2. [2] 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. 128-133
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • A random geometric graph Gd(n, r) is obtained by placing n vertices uniformly andindependently at random in the hypercube [0, 1]d and joining two vertices by an edge ifthe distance between them is at most r. We study the problem of the containment of k-thpowers of Hamilton cycles in the union of Gd(n, r) with an n-vertex graph Hn with minimumdegree αn. For all values of k, d and α, we provide asymptotically optimal values for rwhich ensure the union contains the k-th power of a Hamilton cycle with high probability.Our result implies asymptotically optimal conditions for the containment of other spanningstructures.