Efficient enumeration of graceful permutations

Research paper by Michal Adamaszek

Indexed on: 21 Aug '06Published on: 21 Aug '06Published in: Mathematics - Combinatorics


A graceful n-permutation is a graceful labeling of an n-vertex path P_n. In this paper we improve the asymptotic lower bound on the number of such permutations from (5/3)^n to 2.37^n. This is a computer-assisted proof based on an effective algorithm that enumerates graceful n-permutations. Our algorithm is also presented in detail.