The phrase "are necessary for complete" is not correct as it is incomplete and lacks a noun to follow "complete." You can use it when discussing requirements or components needed for something to be whole or finished, but it needs to be part of a complete sentence.
Example: "These resources are necessary for complete understanding of the topic."
Alternatives: "are essential for total" or "are required for full".
For a cycle of N vertices, we show that at least four test rounds are necessary for complete diagnosis if N is not a multiple of three.
The ChIP experiments revealed that both Adr1 and Cat8 are inherently capable of recruiting each coactivator individually (i.e. no coactivator is absolutely dependent on both Adr1 and Cat8 for recruitment) (Fig. 1, and discussion); however, both are necessary for complete chromatin remodeling.
Both TL and EOO are necessary for complete vulnerability scores.
The results clearly indicate that both the mechanisms are necessary for complete repression at high glucose concentrations.
Unfortunately, no published studies exist that have evaluated how many applications of glyphosate are necessary for complete Phragmites control.
This kind of diversity of TCR is necessary for complete immunisation coverage.
Addition of a binder was necessary for complete crack free components.
This is a form of critical behavior and can lead to ignition conditions, which is necessary for complete regeneration.
After embolization, gentle additional compression was necessary for complete occlusion, with a mean duration of 6.3 minutes (range, 0 to 15 minutes), except in one case with treatment with abciximab in which it was 45 minutes.
NOTE: forget about the length of the paper; the thesis should be as long as it needs to be; put extraneous information (stuff that the reader doesn't necessarily want to read, yet that is necessary for complete clarity of your methods and procedures) in appendices -- this may include raw data, methodology.
In one case hardware removal was necessary for complete healing.
