Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: List coloring of matroids and base exchange properties   A coloring of a matroid is an assignment of colors to the elements of its
ground set. We restrict to proper colorings - those for which elements of the
same color form an independent set. Seymour proved that a $k$-colorable matroid
is also colorable from any lists of size $k$. We generalize this theorem to the
case when lists have still fixed sizes, but not necessarily equal. For any
fixed size of lists assignment $\ell$, we prove that, if a matroid is colorable
from a particular lists of size $\ell$, then it is colorable from any lists of
size $\ell$. This gives an explicit necessary and sufficient condition for a
matroid to be list colorable from any lists of a fixed size. As an application,
we show how to use our condition to derive several base exchange properties.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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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: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: math-ph