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  1.  14
    Domatic Partitions of Computable Graphs.Matthew Jura, Oscar Levin & Tyler Markkanen - 2014 - Archive for Mathematical Logic 53 (1-2):137-155.
    Given a graph G, we say that a subset D of the vertex set V is a dominating set if it is near all the vertices, in that every vertex outside of D is adjacent to a vertex in D. A domatic k-partition of G is a partition of V into k dominating sets. In this paper, we will consider issues of computability related to domatic partitions of computable graphs. Our investigation will center on answering two types of questions for (...)
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  2.  3
    The Computational Strength of Matchings in Countable Graphs.Stephen Flood, Matthew Jura, Oscar Levin & Tyler Markkanen - 2022 - Annals of Pure and Applied Logic 173 (8):103133.
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  3.  11
    Reverse Mathematics and the Coloring Number of Graphs.Matthew Jura - 2016 - Notre Dame Journal of Formal Logic 57 (1):27-44.
    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 $G=$ 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 $n$ (...)
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  4.  10
    A-Computable Graphs.Matthew Jura, Oscar Levin & Tyler Markkanen - 2016 - Annals of Pure and Applied Logic 167 (3):235-246.