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Moreover, any constructive proof of Tucker’s lemma provides algorithmic interpretations of these results. We present a constructive proof of Ky Fan’s combinatorial lemma concerning labellings of triangulated spheres. We also give a direct proof for the same tightness result. We remark that the same kind of technique is used with other complexes related to graphs, too. Such graphs include Kneser graphs, their vertex color-critical subgraphs, the Schrijver (or stable Kneser) graphs; Mycielski graphs, and their generalizations; and Borsuk graphs. Other, closely related examples are provided by Schrijver graphs, that are vertex color-critical induced subgraphs of Kneser graphs, and many of the so-called generalized Mycielski graphs. Kneser graphs that are vertex-critical with respect to the chromatic number. Kneser and Schrijver graphs. We also show that odd chromatic Schrijver graphs behave differently, their circular chromatic number can be arbitrarily close to the other extreme. ≥ 4 but Theorem 3 claims the existence of Schrijver graphs with smaller local than ordinary chromatic number only with chromatic number 5555 and up. As a second application of wide colorings we prove in Subsection 4.3 that Theorem Personalized space jam Air Force 1 Hiking Shoes is also tight for several generalized Mycielski graphs. Borsuk graphs. In Subsection 4.4 we prove that the local chromatic number of Borsuk graphs behaves similarly as that of the graphs already mentioned above