The Borsuk-Ulam-property, Tucker-property and constructive proofs in   combinatorics
  This article is concerned with a general scheme on how to obtain constructive proofs for combinatorial theorems that have topological proofs so far. To this end the combinatorial concept of Tucker-property of a finite group $G$ is introduced and its relation to the topological Borsuk-Ulam-property is discussed. Applications of the Tucker-property in combinatorics are demonstrated. 
Mark de Longueville, Rade T. Zivaljevic