Notre Dame Journal of Formal Logic

Reverse Mathematics and the Coloring Number of Graphs

Matthew Jura

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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 G=(V,E) is the least cardinal κ such that there is a well-ordering of V for which below any vertex in V there are fewer than κ many vertices connected to it by E. We will study a theorem due to Komjáth and Milner, stating that if a graph is the union of n forests, then the coloring number of the graph is at most 2n. We focus on the case when n=1.

Article information

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

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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

reverse mathematics coloring number graph computability theory


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.

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