Graphs without repeated cycle lengths

dc.creatorLai, Chunhui
dc.date2003-05-12
dc.date.accessioned2026-07-07T04:57:55Z
dc.date.available2026-07-07T04:57:55Z
dc.descriptionIn 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.description5 pages
dc.identifierhttps://arxiv.org/abs/math/0305161
dc.identifierhttp://arxiv.org/abs/math/0305161
dc.identifierAustralasian Journal of Combinatorics 27 2003 101-105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67434
dc.subjectCombinatorics
dc.subject05C38, 05C35
dc.titleGraphs without repeated cycle lengths
dc.typetext

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