Lovasz Theta

I believe that Robert Samal has conjectured a version of this for the Lovasz $ \vartheta $ function, i.e. that \[\bar{\vartheta}(G \times H) = \min\{\bar{\vartheta}(G), \bar{\vartheta}(H)\}\] where $ \bar{\vartheta}(G) := \vartheta(\overline{G}) $. I can't find it in the Garden, but it is in this presentation by Samal: http://iuuk.mff.cuni.cz/research/cmi/cmi-I-Samal.pdf


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