On the size of graphs with all cycles having distinct length
By \(f(n)\) the author means the maximum number of edges in a graph of order \(n\) in which no two cycles have the same length. In the book of \textit{J. A. Bondy} and \textit{U. S. R. Murty} [Graph theory with applications (1976)] one finds Erdős' question of determining \(f(n)\). In the paper under review it is shown that if \(t\) is positive integer then \(f(n)\geq n+9t-1\) for \(n\geq 36.5t^ 2-4.5t+1\). Finally it is conjectured that \(\lim(f(n)-n)/\sqrt n\leq\sqrt 3\).
scientific article; zbMATH DE number 500653