On The Independence Number Of Random Interval Graphs

A random interval graph of order n is generated by picking 2n numbers X 1 : : : X 2n independently from the uniform distribution on 0; 1] and considering the collection of n intervals with extremities X 2i?1 and X 2i for i 2 f1;:::ng. The graph vertices correspond to intervals. Two vertices are connected if the corresponding intervals intersect. This paper characterizes the uctuations of the independence number in random interval graphs. This characterization is obtained through the analysis of the greedy algorithm. We actually prove limit theorems (central limit theorem and large deviation principle) on the number of phases of this greedy algorithm. The proof relies on the analysis of rst-passage-times through a random level.