A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length

Details A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length

2002-06-06

arxiv.org/abs/math/0206050v2

The Electronic Journal of Combinatorics 8(2001), #N9

Mathematics

Combinatorics

6 pages

Scientific paper

In 1975, P. Erd\"{o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph of $n$ vertices in which any two cycles are of different lengths. In this paper, it is proved that $$f(n)\geq n+32t-1$$ for $t=27720r+169 (r\geq 1)$ and $n\geq{6911/16}t^{2}+{514441/8}t-{3309665/16}$. Consequently, $\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2562 \over 6911}}.$

Affiliated with

Also associated with

No associations

Rating

A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-436101