# Topology of Hom complexes and test graphs for bounding chromatic number

@article{Dochtermann2009TopologyOH, title={Topology of Hom complexes and test graphs for bounding chromatic number}, author={A. Dochtermann and C. Schultz}, journal={Israel Journal of Mathematics}, year={2009}, volume={187}, pages={371-417} }

The Hom complex of homomorphisms between two graphs was originally introduced to provide topological lower bounds on the chromatic number. In this paper we introduce new methods for understanding the topology of Hom complexes, mostly in the context of Γ-actions on graphs and posets (for some group Γ). We view the Hom(T, ⊙) and Hom(⊙, G) complexes as functors from graphs to posets, and introduce a functor (⊙)1 from posets to graphs obtained by taking atoms as vertices. Our main structural… CONTINUE READING

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