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- W1976760940 abstract "A fundamental result in structural graph theory states that every graph with large average degree contains a large complete graph as a minor. We prove this result with the extra property that the minor is small with respect to the order of the whole graph. More precisely, we describe functions $f$ and $h$ such that every graph with $n$ vertices and average degree at least $f(t)$ contains a $K_t$-model with at most $h(t)cdotlog n$ vertices. The logarithmic dependence on $n$ is best possible (for fixed $t$). In general, we prove that $f(t)leq 2^{t-1}+eps$. For $tleq 4$, we determine the least value of $f(t)$; in particular $f(3)=2+eps$ and $f(4)=4+eps$. For $tleq4$, we establish similar results for graphs embedded on surfaces, where the size of the $K_t$-model is bounded (for fixed $t$)." @default.
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- W1976760940 date "2012-08-01" @default.
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- W1976760940 title "Small minors in dense graphs" @default.
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- W1976760940 doi "https://doi.org/10.1016/j.ejc.2012.02.003" @default.
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