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

dc.creatorLai, Chunhui
dc.date2002-06-06
dc.date2002-06-07
dc.date.accessioned2026-07-07T04:48:55Z
dc.date.available2026-07-07T04:48:55Z
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 $$f(n)\geq n+32t-1$$ for $t=27720r+169 (r\geq 1)$ and $n\geq{6911/16}t^{2}+{514441/8}t-{3309665/16}$. Consequently, $\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2562 \over 6911}}.$
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0206050
dc.identifierhttp://arxiv.org/abs/math/0206050
dc.identifierThe Electronic Journal of Combinatorics 8(2001), #N9
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64235
dc.subjectCombinatorics
dc.subject05C38, 05C35
dc.titleA Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length
dc.typetext

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