  We propose a novel approach for bounding the probability of error of discrete
memoryless channels with a zero-error capacity based on a combination of
Lov\'asz' and Gallager's ideas. The obtained bounds are expressed in terms of a
function $\vartheta(\rho)$, introduced here, that varies from the cut-off rate
of 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 present
form, is finite for all rates larger than the Lov\'asz theta function.
