Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The extremal function for $K_9^=$ minors   We prove the extremal function for $K_9^=$ minors, where $K_9^=$ denotes the
complete graph $K_9$ with two edges removed. In particular, we show that any
graph with $n$ vertices and at least $6n - 20$ edges either contains a $K_9^=$
minor or is isomorphic to a graph obtained from disjoint copies of $K_8$ and
$K_{2, 2, 2, 2, 2}$ by identifying cliques of size 5. We utilize computer
assistance to prove one of our lemmas.

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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: cs