Edge disjoint Hamilton cycles in graphs

Let G be a graph of order n and k greater than or equal to 0 an integer. It is conjectured in [8] that if for any two vertices u and v of a 2(k+ 1)-co nnected graph G,d(G)(u,v)= 2 implies that max{d(u;G),d(v;G)}greater than or equal to (n/2)+ 2k, then G has k + 1 edge disjoint Hamilton cycles. This c onjecture is true for k= 0,1 (see of. [3] and [8]), It will be proved in th is paper that the conjecture is true for every integer k greater than or eq ual to 0, (C) 2000 John Wiley & Sons, Inc.