Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coloring graphs with no even hole $\geq 6$: the triangle-free case   In this paper, we prove that the class of graphs with no triangle and no
induced cycle of even length at least 6 has bounded chromatic number. It is
well-known that even-hole-free graphs are $\chi$-bounded but we allow here the
existence of $C_4$. The proof relies on the concept of Parity Changing Path, an
adaptation of Trinity Changing Path which was recently introduced by Bonamy,
Charbit and Thomass\'e to prove that graphs with no induced cycle of length
divisible by three have bounded chromatic number.

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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th