Lower bound for the size of maximal nontraceable graphs

Abstract

Let g(n) denote the minimum number of edges of a maximal nontraceable graph of order n. Dudek, Katona and Wojda (2003) showed that g(n) ≥ [3n-2/2] -2 for n ≥ 20 and g(n) ≤ [2n-2/2] for n ≥ 54 as well as for n ∈ I = {22,23,30,31,38,39,40,41,42, 43,46,47,48,49,50,51}. We show that g(n) = [3n-2/2] for n ≥ 54 as well as for n ∈ I ∪ {12,13} and we determine g(n) for n ≤ 9.