The Colouring Number of Infinite Graphs

The Colouring Number of Infinite Graphs

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...

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Veröffentlicht in:Combinatorica (Budapest. 1981) 2019-12, Vol.39 (6), p.1225-1235
Hauptverfasser: Bowler, Nathan, Carmesin, Johannes, Komjáth, Péter, Reiher, Christian
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Coloring
Combinatorics
Graph theory
Mathematics
Mathematics and Statistics
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Beschreibung
Zusammenfassung: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.
ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-019-4045-9