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- W4299272005 abstract "Given a connected graph $G$ on $n$ vertices, with minimum degree $deltageq 2$ and girth at least $g geq 4$, what is the maximum radius $r$ this graph can have? ErdH{o}s, Pach, Pollack and Tuza established in the triangle-free case ($g=4$) that $r leq frac{n-2}{delta}+12$, and noted that up to the value of the additive constant, this is tight. We determine the exact value for the triangle-free case. For higher $g$ little is known. We settle the order of $r$ for $g=6,8,12$ and prove an upper bound to the order for general even $g$. Finally, we show that proving the corresponding lower bound for general even $g$ is equivalent to the ErdH{o}s girth conjecture." @default.
- W4299272005 created "2022-10-02" @default.
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- W4299272005 date "2020-09-01" @default.
- W4299272005 modified "2023-10-17" @default.
- W4299272005 title "Radius, Girth and Minimum Degree" @default.
- W4299272005 doi "https://doi.org/10.48550/arxiv.2009.00741" @default.
- W4299272005 hasPublicationYear "2020" @default.
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