Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs with large chromatic number induce $3k$-cycles   Answering a question of Kalai and Meshulam, we prove that graphs without
induced cycles of length $3k$ have bounded chromatic number. This implies the
very first case of a much broader question asserting that every graph with
large chromatic number induces a graph $H$ such that the sum of the Betti
numbers of the independence complex of $H$ is also large.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
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The categories of this paper are: nucl-th