The maximum edge count of a triangle-free graph on n vertices that must contain a prescribed triangle-free P is bounded above by nα(P)/2 and below by a Shearer-type expression, yielding Θ(n² ln d/d) for constrained P.
The triangle-free process
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Sabotage the Mantel Theorem
The maximum edge count of a triangle-free graph on n vertices that must contain a prescribed triangle-free P is bounded above by nα(P)/2 and below by a Shearer-type expression, yielding Θ(n² ln d/d) for constrained P.