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We identify three 3-graphs on five vertices each missing in all knownextremal configurations for Turan's (3,4)-problem and prove Turan's conjecturefor 3-graphs that are additionally known not to contain any induced copies ofthese 3-graphs. Our argument is based on an (apparently) new technique of"indirect interpretation" that allows us to retrieve additional structure fromhypothetical counterexamples to Turan's conjecture, but in rather loose andlimited sense. We also include two miscellaneous calculations in flag algebrasthat prove similar results about some other additional forbidden subgraphs.

On Turan's (3,4)-problem with forbidden configurations