Geodesic
A lower bound for the number of edges in a graph containing no two cycles of the same length
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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In 1975, P. Erdős proposed the problem of determining the maximum number $f(n)$ of edges in a simple 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 $n\geq {{6911}\over {16}}t^{2}+{{514441}\over {8}}t-{{3309665}\over {16}}$. Consequently, $\liminf _{n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2562 \over 6911}}.$
DOI : 10.37236/1594
Classification : 05C38, 05C35
Mots-clés : cycle length 
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     title = {A lower bound for the number of edges in a graph containing no two cycles of the same length},
     journal = {The electronic journal of combinatorics},
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     doi = {10.37236/1594},
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Chunhui Lai. A lower bound for the number of edges in a graph containing no two cycles of the same length. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1594

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