We give a proof of Enomoto's conjecture for graphs of sufficiently large order. Enomoto's conjecture states that: if G is a graph of order n with minimum degree at least n/2+ 1, then for any pair x,y of vertices of G, there is a Hamiltonian cycle C of G such that the distance between x and y in C is n/2.

The main tools of our proof are Regularity Lemma of Szemeredi and Blow-up Lemma of Koml os et al..

This is a joint work with Weihua He and Hao Li.