Any n-vertex 3-graph with minimum codegree at least ⌊n/3⌋
must have a spanning tight component, but immediately below this threshold it
is possible for no tight component to span more than ⌈2n/3⌉
vertices. Motivated by this observation, we ask which codegree forces a tight
component of at least any given size. The corresponding function seems to have
infinitely many discontinuities, but we provide upper and lower bounds, which
asymptotically converge as the function nears the origin.Comment: 10 pages. Final version accepted by European J. Combi