The colouring number of infinite graphs
Combinatorics
2018-07-05 v2
Abstract
We show that, given an infinite cardinal , a graph has colouring number at most 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.
Keywords
Cite
@article{arxiv.1512.02911,
title = {The colouring number of infinite graphs},
author = {Nathan Bowler and Johannes Carmesin and Péter Komjáth and Christian Reiher},
journal= {arXiv preprint arXiv:1512.02911},
year = {2018}
}