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arXiv · 2008.10260

The list-chromatic number and the coloring number of uncountable graphs

Toshimichi Usuba
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Abstract

We study the list-chromatic number and the coloring number of graphs, especially uncountable graphs. We show that the coloring number of a graph coincides with its list-chromatic number provided that the diamond principle holds. Under the GCH assumption, we prove the singular compactness theorem for the list-chromatic number. We also investigate reflection principles for the list-chromatic number and the coloring number of graphs.

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Toshimichi Usuba. 2020-08-24. The list-chromatic number and the coloring number of uncountable graphs. https://arxiv.org/abs/2008.10260

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