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- W2956095973 abstract "We discuss the length of the longest cycle in a sparse random graph $G_{n,p},p=c/n$. $c$ constant. We show that for large $c$ there is a function $f(c)$ such that $L_n(c)/nto f(c)$ a.s. The function $f(c)=1-sum_{k=1}^infty p_k(c)e^{-kc}$ where $p_k$ is a polynomial in $k$. We are only able to explicitly give the values $p_1,p_2$, although we could in principle compute any $p_k$. We see immediately that the length of the longest path is also asymptotic to $f(c)n$ w.h.p." @default.
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- W2956095973 date "2019-07-08" @default.
- W2956095973 modified "2023-09-27" @default.
- W2956095973 title "A scaling limit for the length of the longest cycle in a sparse random graph" @default.
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