Topology of acyclic complexes of tournaments and coloring

Deniz Z.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, cilt.26, ss.213-226, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 26
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s00200-014-0245-0
  • Dergi Adı: APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Sayfa Sayısı: ss.213-226

Özet

We prove that the acyclic complex of any trisectionable tournament is homotopy equivalent to a wedge of spheres, and show that there exists a fix number such that if is a trisectionable tournament and is the highest dimension of a sphere occurring in such a decomposition for , then the (acyclic) chromatic number of satisfies for some , and by way of an example, we verify that the provided upper bound is tight.