The Lovász Theta Function for Random Regular Graphs and Community Detection in the Hard Regime

SIAM Journal on Computing, pp. 1098-1119, 2019.

Cited by: 1|Bibtex|Views43|DOI:https://doi.org/10.1137/18m1180396
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Abstract:

We derive upper and lower bounds on the degree $d$ for which the Lovu0027asz $vartheta$ function, or equivalently sum-of-squares proofs with degree two, can refute the existence of a $k$-coloring in random regular graphs $G_{n,d}$. We show that this type of refutation fails well above the $k$-colorability transition, and in particular eve...More

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