# The colouring number of infinite graphs

Research paper by Nathan Bowler, Johannes Carmesin, Christian Reiher

Indexed on: 09 Dec '15Published on: 09 Dec '15Published in: Mathematics - Combinatorics

#### Abstract

We show that, given an infinite cardinal $\mu$, a graph has colouring number at most $\mu$ 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.