The Extremal Function for Complete Minors

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Abstract

Let c(t) be the minimum number c such that every graph G with e(G)≥c \G\ contracts to a complete graph Kt. We show that c(t) = (α + o(1))t √log t where α = 0.319... is an explicit constant. Random graphs are extremal graphs. © 2001 Academic Press.

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Thomason, A. (2001). The Extremal Function for Complete Minors. Journal of Combinatorial Theory. Series B, 81(2), 318–338. https://doi.org/10.1006/jctb.2000.2013

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