New eigenvalue bound for the fractional chromatic number

Abstract

AbstractGiven a graph , we let denote the sum of the squares of the positive eigenvalues of the adjacency matrix of , and we similarly define . We prove that and thus strengthen a result of Ando and Lin, who showed the same lower bound for the chromatic number . We in fact show a stronger result wherein we give a bound using the eigenvalues of and whenever has a homomorphism to an edge‐transitive graph . Our proof utilizes ideas motivated by association schemes.