Geodesic
A note on graphs without short even cycles
The electronic journal of combinatorics, Tome 12 (2005)

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Zbl arXiv EuDML
In this note, we show that any $n$-vertex graph without even cycles of length at most $2k$ has at most ${1\over2}n^{1 + 1/k} + O(n)$ edges, and polarity graphs of generalized polygons show that this is asymptotically tight when $k \in \{2,3,5\}$.
DOI : 10.37236/1972
Classification : 05C38, 05C35
Mots-clés : polarity graphs, polygons 
Thomas Lam; Jacques Verstraëte. A note on graphs without short even cycles. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1972
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     author = {Thomas Lam and Jacques Verstra\"ete},
     title = {A note on graphs without short even cycles},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1972},
     zbl = {1060.05057},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1972/}
}
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