Notre Dame Journal of Formal Logic

Reverse Mathematics and the Coloring Number of Graphs

Matthew Jura

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Abstract

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

Source
Notre Dame J. Formal Logic, Volume 57, Number 1 (2016), 27-44.

Dates
Received: 26 October 2011
Accepted: 9 August 2013
First available in Project Euclid: 30 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1443619666

Digital Object Identifier
doi:10.1215/00294527-3321905

Mathematical Reviews number (MathSciNet)
MR3447723

Zentralblatt MATH identifier
1353.03008

Subjects
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

Keywords
reverse mathematics coloring number graph computability theory

Citation

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


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References

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