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2016 Reverse Mathematics and the Coloring Number of Graphs
Matthew Jura
Notre Dame J. Formal Logic 57(1): 27-44 (2016). DOI: 10.1215/00294527-3321905

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.

Citation

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Matthew Jura. "Reverse Mathematics and the Coloring Number of Graphs." Notre Dame J. Formal Logic 57 (1) 27 - 44, 2016. https://doi.org/10.1215/00294527-3321905

Information

Received: 26 October 2011; Accepted: 9 August 2013; Published: 2016
First available in Project Euclid: 30 September 2015

zbMATH: 1353.03008
MathSciNet: MR3447723
Digital Object Identifier: 10.1215/00294527-3321905

Subjects:
Primary: 03B30, 03D80
Secondary: 05C15

Rights: Copyright © 2016 University of Notre Dame

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Vol.57 • No. 1 • 2016
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