xpmachina,
The "complete honesty" approach simply means letting the authorities know that you fully understand that polygraph "testing" is a fraud and that the whole exercise is pointless from the beginning. There may be some legal advantage to doing this (with your lawyer there as a witness).
If the police really believe that you are guilty or otherwise involved, then you run a risk of "failing" the "test" no matter what the polygraph charts look like.
Because of variations in the Relevant/Irrlevant technique (and I am still skeptical as to whether this is indeed the technique that you will encounter), and my lack of familiarity with polygraph techniques as practiced in your country, I really don't feel confident in advising you in this regard.
One factor that seems to be fairly constant in the Relevant/Irrelevant technique as practiced in the United States is that the polygrapher looks for a "consistent, specific, and significant" reaction to a relevant question, no matter how the question is worded and no matter in what order the question is asked. As I mentioned above, such a pattern can be avoided by augmenting one's reactions to a different relevant question during each polygraph chart (which will probably consist of about 10 questions, but could conceivably go on for 15, 25, or even 40 -- even though to my knowledge no polygraph school in the U.S. officially endorses the use of such long question series).
Sometimes, a form of "control" question is asked during a R/I "test." For example, the Keeler Polygraph Institute in Chicago teaches that the "test" should begin with an announcement like, "The test is about to begin." Although this is a statement, not a question, it serves as a sort of "control question" to the extent that the polygrapher expects he might see a reaction to it. A similar announcement is made at the end, "The test is ended" (or words to that effect). Thus, it might be advantageous to someone facing the Keeler R/I technique to create a reaction to the announcement of the beginning and ending of the "test." If one's reactions to the announcements are greater than one's reactions to any of the relevant questions, the polygrapher may be more inclined to decide that the subject is truthful.
Another technique called the
General Question Test once taught by the U.S. Department of Defense Polygraph Institute uses "disguised control" questions. The "test" outwardly appears to consist of only relevant and irrelevant questions, but before any true relevant questions are asked, the polygrapher asks something similar to, "Do you intend to answer all questions truthfully?" and at the end the polygrapher asks "Did you lie to me in any way here today?" Reactions to the relevant questions are compared to reactions to these "disguised control" questions. So here, it would be advantageous to aument one's reactions to the "disguised control" questions.
Another technique that is sometimes used is that if the polygrapher sees no reactions to any relevant or irrelevant questions in a series, he will add a surprise probable-lie "control" question to the end of the series, to see if it produces a reaction. If it does, the polygrapher will be more likely to conclude that the examinee was truthful.
I can't predict what variation of the R/I technique you might encounter, and I wouldn't be surprised if you were to be given a regular probable-lie "control" question "test" or even a Guilty Knowledge Test instead .
Again, however you decide to handle this, I suggest you consult with your lawyer.