# An eigenvalue bound for the fractional chromatic number

@inproceedings{Silva2021AnEB, title={An eigenvalue bound for the fractional chromatic number}, author={Marcel Kenji de Carli Silva and Gabriel Coutinho and Rafael Grandsire}, year={2021} }

We show that Hoffman’s sum of eigenvalues bound for the chromatic number is at least as good as the Lovász theta number, but no better than the ceiling of the fractional chromatic number. In order to do so, we display an interesting connection between this sum of eigenvalues bound and a generalization of the Lovász theta number introduced by Manber and Narasimhan in 1988.

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