In the paging problem we have to manage a two-level memory system, in which the first level has short access time but can hold only up to k pages, while the second level is very large but slow. We use competitive analysis to study the relative performance of two best known algorithms for paging, LRU and FIFO. Sleator and Tarjan proved that the competitive ratio of LRU and FIFO is k. In practice, however, LRU is known to perform much better than FIFO. It is believed that the superiority of LRU can be attributed to locality of reference exhibited in request sequences. In order to study this phenomenon, Borodin, Irani, Raghavan and Schieber refined the competitive approach by introducing the concept of access graphs. They conjectured that the competitive ratio of LRU on each access graph is less than or equal to the competitive ratio of FIFO. We will prove this conjecture.