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arXiv · 1512.02911

The colouring number of infinite graphs

Nathan Bowler·Johannes Carmesin·Péter Komjáth·Christian Reiher
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Abstract

We show that, given an infinite cardinal $μ$, a graph has colouring number at most $μ$ if and only if it contains neither of two types of subgraph. We also show that every graph with infinite colouring number has a well-ordering of its vertices that simultaneously witnesses its colouring number and its cardinality.

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Nathan Bowler, Johannes Carmesin, Péter Komjáth, Christian Reiher. 2018-07-04. The colouring number of infinite graphs. https://arxiv.org/abs/1512.02911

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