Independent Sets of Maximal Size in Tensor Powers of Vertex-Transitive Graphs

摘要

Let G be a connected, nonbipartite vertex-transitive graph. We prove that if the only independent sets of maximal cardinality in the tensor product G x G are the preimages of the independent sets of maximal cardinality in G under projections, then the same holds for all finite tensor powers of G, thus providing an affirmative answer to a question raised by Larose and Tardif (J Graph Theory 40(3) (2002), 162-171).