# The extremal function for structured sparse minors

@inproceedings{Wales2021TheEF, title={The extremal function for structured sparse minors}, author={Matthew Wales}, year={2021} }

Let c(H) be the smallest value for which e(G)/|G| > c(H) implies H is a minor of G. We show a new upper bound on c(H), which improves previous bounds for graphs with a vertex partition where some pairs of parts have many more edges than others — for instance a complete bipartite graph with a small number of edges placed inside one class. We also show a tight matching lower bound for almost all such graphs. We apply these results to show c(Kft/ log t,t) = (0.638 . . .+ of (1))t √ f , for f = o…

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