Reverse Mathematics and Recursive Graph Theory

13 years 4 months ago

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We examine a number of results of inﬁnite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs, Euler paths, and Hamilton paths. Reverse mathematics provides powerful techniques for analyzing the logical content of theorems. By contrast, recursive mathematics analyzes the eﬀective content of theorems. Theorems and techniques of recursive mathematics can often inspire related results in reverse mathematics, as demonstrated by the research presented here. Sections 1 and 2 analyze theorems on graph colorings. Section 3 considers graphs with Euler paths. Stronger axiom systems are introduced and applied to the study of Hamilton paths in Section 4. We assume familiarity with the methods of reverse mathematics, as described in [15]. Additional information, including techniques for encoding mathematical statements in second-order arithmetic, can be...

William I. Gasarch, Jeffry L. Hirst

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