Homology tests for graph colorings
Abstract
We describe a simple homological test for obstructions to graph colorings. The main idea is to combine the framework of Hom-complexes with the following general fact: an arbitrary Z2-space has nontrivial homology with Z2-coefficients in the dimension equal to its Stiefel-Whitney height. Actually, as a result we have a whole family of homology tests, one for each test graph. In general, these tests will give different answers, depending heavily on the choice of the test graph. We illustrate this phenomenon with some examples.
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