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- W4300709811 abstract "Let $kge 1$ be an odd integer, $t=lfloor {{k+2}over 4}rfloor$, and $q$ be a prime power. We construct a bipartite, $q$-regular, edge-transitive graph $C!D(k,q)$ of order $v le 2q^{k-t+1}$ and girth $g ge k+5$. If $e$ is the the number of edges of $C!D(k,q)$, then $e =Omega(v^{1+ {1over {k-t+1}}})$. These graphs provide the best known asymptotic lower bound for the greatest number of edges in graphs of order $v$ and girth at least $g$, $ gge 5$, $g not= 11,12$. For $gge 24$, this represents a slight improvement on bounds established by Margulis and Lubotzky, Phillips, Sarnak; for $5le gle 23$, $gnot= 11,12$, it improves on or ties existing bounds." @default.
- W4300709811 created "2022-10-04" @default.
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- W4300709811 date "1994-12-31" @default.
- W4300709811 modified "2023-10-04" @default.
- W4300709811 title "A new series of dense graphs of high girth" @default.
- W4300709811 doi "https://doi.org/10.48550/arxiv.math/9501231" @default.
- W4300709811 hasPublicationYear "1994" @default.
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