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{\bf Ronald Gould, Tomasz \L uczak and John Schmitt}
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{\bf Constructive Upper Bounds for Cycle-Saturated Graphs of Minimum Size}
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A graph $G$ is said to be $C_l$-saturated if $G$ contains no cycle of
length $l$, but for any edge in the complement of $G$ the graph $G+e$
does contain a cycle of length $l$. The minimum number of edges of a
$C_l$-saturated graph was shown by Barefoot et al. to be between
$n+c_1{n\over l}$ and $n+c_2{n\over l}$ for some positive constants
$c_1$ and $c_2$. This confirmed a conjecture of Bollob\'as. Here we
improve the value of $c_2$ for $l \geq 8$.
\bye