Geodesic
An extremal theorem in the hypercube
The electronic journal of combinatorics, Tome 17 (2010)
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The hypercube $Q_n$ is the graph whose vertex set is $\{0,1\}^n$ and where two vertices are adjacent if they differ in exactly one coordinate. For any subgraph $H$ of the cube, let $\textrm{ex}(Q_n, H)$ be the maximum number of edges in a subgraph of $Q_n$ which does not contain a copy of $H$. We find a wide class of subgraphs $H$, including all previously known examples, for which $\textrm{ex}(Q_n, H) = o(e(Q_n))$. In particular, our method gives a unified approach to proving that $\textrm{ex}(Q_n, C_{2t}) = o(e(Q_n))$ for all $t \geq 4$ other than $5$.
DOI : 10.37236/383
Classification : 05C35, 05C38, 05D99 
@article{10_37236_383,
     author = {David Conlon},
     title = {An extremal theorem in the hypercube},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/383},
     zbl = {1193.05094},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/383/}
}
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David Conlon. An extremal theorem in the hypercube. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/383

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