PATTERN COLORED HAMILTON CYCLES IN RANDOM GRAPHS.

We consider the existence of patterned Hamilton cycles in randomly colored random graphs. Given a string π over a set of colors { 1, 2, . . . , r}, we say that a Hamilton cycle is π -colored if the pattern repeats at intervals of length |π| as we go around the cycle. We prove a hitting time result for the existence of such a cycle. We also prove a hitting time result for the related notion of π -connected. [ABSTRACT FROM AUTHOR]