Geodesic
Constructive upper bounds for cycle-saturated graphs of minimum size
The electronic journal of combinatorics, Tome 13 (2006)
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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 Bollobás. Here we improve the value of $c_2$ for $l \geq 8$.
DOI : 10.37236/1055
Classification : 05C35, 05C38 
@article{10_37236_1055,
     author = {Ronald Gould and Tomasz {\L}uczak and John Schmitt},
     title = {Constructive upper bounds for cycle-saturated graphs of minimum size},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1055},
     zbl = {1086.05039},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1055/}
}
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Ronald Gould; Tomasz Łuczak; John Schmitt. Constructive upper bounds for cycle-saturated graphs of minimum size. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1055

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