Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Induced subgraphs of induced subgraphs of large chromatic number   We prove that, for every graph $F$ with at least one edge, there is a
constant $c_F$ such that there are graphs of arbitrarily large chromatic number
and the same clique number as $F$ in which every $F$-free induced subgraph has
chromatic number at most $c_F$. This generalises recent theorems of Bria\'nski,
Davies and Walczak, and Carbonero, Hompe, Moore and Spirkl. Moreover, we show
an analogous statement where clique number is replaced by odd girth.

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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph