By Zach Abel
Answer: SLARTIBARTFAST COUGHED POLITELY
First, cut out the strips of each color and attach them end-to-end (each strip starts where the previous one left off), resulting in four long, monochromatic strips of varying length. By folding along the provided crease lines, the strips become orthogonal paths with all letters oriented in the same direction. Furthermore, each strip begins and ends at the same letter in the same location, so each should be joined into a cycle. The resulting cycles are as follows:
The horizontal portions are beginning to form words, and some experimentation shows that they can be overlayed to mostly spell a complete message. Finishing the message requires weaving the strips above and below each other to reveal the correct letters. Here is the result, and the resulting message:
THE NUMBERS P Q R AND X Y Z DEFINED IN THE PUZZLE ARE THE LINKING NUMBERS OF THE CORRESPONDING LOOPS AS IN KNOT THEORY. TO EXTRACT THE ANSWER PLEASE READ LINE PQR OF PAGE XYZ IN THE ULTIMATE HITCHHIKERS GUIDE TO THE GALAXY. A COPY OF THE BOOK CAN BE FOUND IN THE MATHCAMP LIBRARY. BEST OF LUCK.
Notice that the strips are colored the same as the vertices of the provided graph, and in fact, the cycles take the shape of their corresponding letters in this graph. The edge labels p,q,r,x,y,z are therefore the linking numbers of the corresponding pairs of loops. Computing these linking numbers (see Wikipedia: Linking number for a formula) gives (p,q,r,x,y,z)=(0,0,7,1,3,1). Line 7 of page 131 of The Ultimate Hitchhiker's Guide to the Galaxy (as found in the camp library) reveals the answer: "Slartibartfast coughed politely."
Note: the covered letters spell out "THIS IS A RED HERRING OR AN ORANGE BABELFISH".