5 research outputs found
An old problem of Erd\H{o}s: a graph without two cycles of the same length
In 1975, P. Erd\H{o}s proposed the problem of determining the maximum number
of edges in a graph on vertices in which any two cycles are of
different lengths. Let be the maximum number of edges in a simple
graph on vertices in which any two cycles are of different lengths. Let
be the set of simple graphs on vertices in which any two cycles are
of different lengths and with the edges of . Let be the
maximum cycle length for all . In this paper, it is proved that for
sufficiently large, . We make the following
conjecture:
Comment: 6 page