Topology of acyclic complexes of tournaments and coloring

Deniz Z.

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol.26, pp.213-226, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26
  • Publication Date: 2015
  • Doi Number: 10.1007/s00200-014-0245-0
  • Title of Journal : APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
  • Page Numbers: pp.213-226

Abstract

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.