Graphs without repeated cycle lengths
| dc.creator | Lai, Chunhui | |
| dc.date | 2003-05-12 | |
| dc.date.accessioned | 2026-07-07T04:57:55Z | |
| dc.date.available | 2026-07-07T04:57:55Z | |
| dc.description | In 1975, P. Erdös 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.} $$\lim_{n \to \infty} {f(n)-n\over \sqrt n}=\sqrt {2.4}.$$ | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305161 | |
| dc.identifier | http://arxiv.org/abs/math/0305161 | |
| dc.identifier | Australasian Journal of Combinatorics 27 2003 101-105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67434 | |
| dc.subject | Combinatorics | |
| dc.subject | 05C38, 05C35 | |
| dc.title | Graphs without repeated cycle lengths | |
| dc.type | text |