Sounds like you just bought the bike? Has it done this since you bought it or did this problem recently appear?
If its done it since you bought it, you may need to go through the carbs. Seems that the vmax carbs cause grief for lots of guys. The nice thing about them is that they are dead easy to remove compared to other bikes and there is plenty of info on this site to help you out.
As far as your exhaust goes, its not uncommon to see some color change near the heads. Especially on the rear headers, right in front of the battery.
If it were my bike I would pull the carbs off and see what's going on in there. You never know what the previous owner did, or didn't do. Before pulling them, check the tank for rust, drain all the float bowls and check for sediment, pull the plugs and inspect the color.
Check the carburator forum here. There are "stickys" that will give you all the info you need to know about how to remove the carbs from the bike, how to change jets, and how to completely tear the carbs down.
You should verify what jets you have in there for the main and paj's. Check the slides for holes, check the needles to see if they are stock or adjustable. Clean everything. Pay special attention to the jet block under the floats. The pilot jet is in there and it is very common to find it blocked.
There is another sticky with carb setups posted. Its pretty common for guys with a full aftermarket exhaust to be running 150 or 147.5 main jets, all other jets stock, shim the needle a little bit, and turn the A/F screws to 2.5-3.5 turns out. That is a starting point, every bike is different but that is a good base line to start.
If you want to get the most you can out of the bike you could always buy a jet kit. There are only 2 of them worth spending your resources on. A dynojet stage 7 or a muscle jet kit. Either can be purchased from Sean Morlery (see banner at top of the forum "morleys muscle). They both have similar top end power. The muscle jet kit will give you more mid range than the stage 7, plus it is a bit cheaper. Neither is a necessity but if you're looking for a few more ponies it will help.
Check out this section of the forum:
http://www.vmaxforum.net/forumdisplay.php?f=6
Spend some time on the stickies. There are threads in here that will show you:
How to remove carbs and change the main jets
How to set the float level. VERY important and its usually off
How to identify jets.
How to identify needles
How to completely rebuild the carbs (6 different how to threads)
How to sync the carbs. Very important and very easy!
Compare settings with other members
Plus much more.
