Graphs without repeated cycle lengths

Details Graphs without repeated cycle lengths Graphs without repeated cycle lengths

2003-05-12

arxiv.org/abs/math/0305161v1

Australasian Journal of Combinatorics 27 2003 101-105

Mathematics

Combinatorics

5 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 $$f(n)\geq n+36t$$ for $t=1260r+169 (r\geq 1)$ and $n \geq 540t^{2}+{175811/2}t+{7989/2}$. Consequently, $\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2 \over 5}}.$ We make the following conjecture: \par \bigskip \noindent{\bf Conjecture.} $$\lim_{n \to \infty} {f(n)-n\over \sqrt n}=\sqrt {2.4}.$$

Affiliated with

Also associated with

No associations

Rating

Graphs without repeated cycle lengths 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 Graphs without repeated cycle lengths, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graphs without repeated cycle lengths will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-202579