## Notre Dame Journal of Formal Logic

### Reverse Mathematics and the Coloring Number of Graphs

Matthew Jura

#### 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 $\kappa$ such that there is a well-ordering of $V$ for which below any vertex in $V$ there are fewer than $\kappa$ 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

#### 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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