# Which graphs can be counted in $C_4$-free graphs?

@inproceedings{Conlon2021WhichGC, title={Which graphs can be counted in \$C\_4\$-free graphs?}, author={David Conlon and Jacob Fox and Benny Sudakov and Yufei Zhao}, year={2021} }

For which graphs F is there a sparse F -counting lemma in C4-free graphs? We are interested in identifying graphs F with the property that, roughly speaking, if G is an n-vertex C4free graph with on the order of n edges, then the density of F in G, after a suitable normalization, is approximately at least the density of F in an ǫ-regular approximation of G. In recent work, motivated by applications in extremal and additive combinatorics, we showed that C5 has this property. Here we construct a…

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