Hom complexes and hypergraph colorings
Kouyemon Iriye, Daisuke Kishimoto · Topology and its Applications · 2013
Babson and Kozlov (2006) [2] studied Hom -complexes of graphs with a focus on graph colorings. In this paper, we generalize Hom -complexes to r -uniform hypergraphs (with multiplicities) and study them mainly in connection with hypergraph colorings. We reinterpret a result of Alon, Frankl and Lovász (1986) [1] by Hom -complexes and show a hierarchy of known lower bounds for the chromatic numbers of r -uniform hypergraphs (with multiplicities) using Hom -complexes.