Homomorphism complexes and -cores |
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Authors: | Greg Malen |
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Institution: | Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA |
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Abstract: | For any fixed graph , we prove that the topological connectivity of the graph homomorphism complex Hom() is at least , where , for the minimum degree of a vertex in a subgraph . This generalizes a theorem of C?uki? and Kozlov, in which the maximum degree was used in place of , and provides a high-dimensional analogue of the graph theoretic bound for chromatic number, , as . Furthermore, we use this result to examine homological phase transitions in the random polyhedral complexes Hom when for a fixed constant . |
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Keywords: | Hom-complexes Degeneracy Random polyhedral complexes |
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