2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106046Combining Ky Fan's theorem with ideas of Greene and Matousek we prove a generalization of Dol'nikov's theorem. Using another variant of the Borsuk-Ulam theorem due to Bacon and Tucker, we also prove the presence of all possible completely multicolored t-vertex complete bipartite graphs in t-colored t-chromatic Kneser graphs and in several of their relatives. In particular, this implies a generalization of a recent result of G. Spencer and F. E. Su.16 pagesCombinatoricsAlgebraic Topology05C15text