Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 57, Number 1 (2016), 27-44.
Reverse Mathematics and the Coloring Number of Graphs
We use methods of reverse mathematics to analyze the proof theoretic strength of a theorem involving the notion of coloring number. Classically, the coloring number of a graph is the least cardinal such that there is a well-ordering of for which below any vertex in there are fewer than many vertices connected to it by . We will study a theorem due to Komjáth and Milner, stating that if a graph is the union of forests, then the coloring number of the graph is at most . We focus on the case when .
Notre Dame J. Formal Logic, Volume 57, Number 1 (2016), 27-44.
Received: 26 October 2011
Accepted: 9 August 2013
First available in Project Euclid: 30 September 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 03D80: Applications of computability and recursion theory
Secondary: 05C15: Coloring of graphs and hypergraphs
Jura, Matthew. Reverse Mathematics and the Coloring Number of Graphs. Notre Dame J. Formal Logic 57 (2016), no. 1, 27--44. doi:10.1215/00294527-3321905. https://projecteuclid.org/euclid.ndjfl/1443619666