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We propose a novel approach for bounding the probability of error of discretememoryless channels with a zero-error capacity based on a combination ofLov\'asz' and Gallager's ideas. The obtained bounds are expressed in terms of afunction $\vartheta(\rho)$, introduced here, that varies from the cut-off rateof the channel to the Lov\'azs theta function as $\rho$ varies from 1 to$\infty$ and which is intimately related to Gallager's expurgated coefficient.The obtained bound to the reliability function, though loose in its presentform, is finite for all rates larger than the Lov\'asz theta function.

An "Umbrella" Bound of the Lov\'asz-Gallager Type