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)\geq\ceil{(3n-2)/2}-2 for n\geq 20 and g(n)\leq\ceil{(3n-2)/2} for n\geq 54 as well as for n\in I={22,23,30,31,38,39, 40,41,42,43,46,47,48,49,50,51}. We show that g(n)=\ceil{(3n-2)/2} for n\geq 54 as well as for n\in I\cup{12,13} and we determine g(n) for n\leq 9.Comment: 10 pages, 3 figure