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Showing 4 of 4 papers in Discrete Mathematics And Combinatorics
In 1975, P. Erd\"{o}s proposed the problem of determining themaximum number $f(n)$ of edges in a graph of $n$ vertices inwhich 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}+\frac{175811}{2}t+\frac{798…
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…
Let f(n) denote the maximum possible number of edges in an n-vertex graph containing no cycles of equal length. The problem of determining f(n) was posed by Erdos in 1975. This paper provides a lower bound for f(n).
Pascal's triangle is the triangular arrangement of binomial coefficients, from which one can obtain the Fibonacci sequence and the golden ratio (approximately 1.618). A question arises: Can the silver ratio (approximately 2.414) be obtained from Pascal's triangle? This paper first establishes a Maxi…
