Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Induced subgraphs of graphs with large chromatic number. VI. Banana
  trees   We investigate which graphs H have the property that in every graph with
bounded clique number and sufficiently large chromatic number, some induced
subgraph is isomorphic to a subdivision of H. In an earlier paper, one of us
proved that every tree has this property; and in another earlier paper with M.
Chudnovsky, we proved that every cycle has this property. Here we give a common
generalization. Say a banana is the union of a set of paths all with the same
ends but otherwise disjoint. We prove that if H is obtained from a tree by
replacing each edge by a banana then H has the property mentioned. We also find
some other multigraphs with the same property.

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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org