Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extracting list colorings from large independent sets   We take an application of the Kernel Lemma by Kostochka and Yancey to its
logical conclusion. The consequence is a sort of magical way to draw
conclusions about list coloring (and online list coloring) just from the
existence of an independent set incident to many edges. We use this to prove an
Ore-degree version of Brooks' Theorem for online list-coloring. The Ore-degree
of an edge $xy$ in a graph $G$ is $\theta(xy) = d_G(x) + d_G(y)$. The
Ore-degree of $G$ is $\theta(G) = \max_{xy\in E(G)}\theta(xy)$. We show that
every graph with $\theta\ge18$ and $\omega\le\frac{\theta}{2}$ is online
$\left\lfloor \frac{\theta}{2}\right\rfloor $-choosable. In addition, we prove
an upper bound for online list-coloring triangle-free graphs:
$\chi_{OL}\le\Delta+1-\lfloor\frac{1}{4}\lg(\Delta)\rfloor$. Finally, we
characterize Gallai trees as the connected graphs $G$ with no independent set
incident to at least $|G|$ edges.

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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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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: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat