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# A LOWER BOUND OF THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH

Submit Time: 2022-05-14
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Institute: 1.闽南师范大学数学与统计学院;

## Abstracts

 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 $$f(n)\geq n+32t-1$$ for $t=27720r+169 \,\ (r\geq 1)$  and $n\geq\frac{6911}{16}t^{2}+\frac{514441}{8}t-\frac{3309665}{16}$. Consequently, $\liminf\sb {n \to \infty} {f(n)-n \over \sqrt n} \geq \sqrt {2 + {2562 \over 6911}}.$
From: Chunhui LAI
Journal:Electronic Journal of Combinatorics 8(1)(2001), #N9
Recommended references： Lai, Chunhui.(2022).不包含两个相同长度的循环的图形中边数的下限.Electronic Journal of Combinatorics 8(1)(2001), #N9.doi:https://doi.org/10.37236/1594 (Click&Copy)
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