# Ordered graphs and large bi-cliques in intersection graphs of curves

@article{Pach2019OrderedGA, title={Ordered graphs and large bi-cliques in intersection graphs of curves}, author={J. Pach and Istv{\'a}n Tomon}, journal={Eur. J. Comb.}, year={2019}, volume={82} }

An ordered graph $G_<$ is a graph with a total ordering $<$ on its vertex set. A monotone path of length $k$ is a sequence of vertices $v_1<v_2<\ldots<v_k$ such that $v_iv_{j}$ is an edge of $G_<$ if and only if $|j-i|=1$. A bi-clique of size $m$ is a complete bipartite graph whose vertex classes are of size $m$.
We prove that for every positive integer $k$, there exists a constant $c_k>0$ such that every ordered graph on $n$ vertices that does not contain a monotone path of length $k$ as an… Expand

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