Non-repeated cycle lengths and Sidon sequences
نویسندگان
چکیده
We prove a conjecture of Boros, Caro, Füredi and Yuster on the maximum number edges in 2-connected graph without repeated cycle lengths, which is restricted version longstanding problem Erd?s. Our proof together with matched lower bound construction Füuredi show that this can be conceptually reduced to seminal finding Sidon sequences theory.
منابع مشابه
Graphs without repeated cycle lengths
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) ≥ n + 36t for t = 1260r + 169 (r ≥ 1) and n ≥ 540t2 + 175811 2 t + 7989 2 . Consequently, lim infn→∞ f(n)−n √ n ≥ √
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2021
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-021-2222-1