Effective Matchmaking (Recursion Theoretic Aspects of a Theorem of Philip Hall)

Manaster, Alfred B.; Rosenstein, Joseph G.

doi:10.1112/plms/s3-25.4.615

Cited by 48 publications

(16 citation statements)

References 7 publications

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“…If e = (x, v} G E, we say x and j> meet e. A matching M is a set of edges so that each node meets at most one edge in M. The following theorem is then easily seen to be equivalent to Theorem II. We note that when put in this graph theoretic context, our counterexamples can be seen to be related to the work of Manaster and Rosenstein [6].…”

Section: Introductionmentioning

confidence: 98%

On the effectiveness of the Schröder-Bernstein theorem

Remmel¹

1981

Proc. Amer. Math. Soc.

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Section: Introductionmentioning

confidence: 98%

On the effectiveness of the Schröder-Bernstein theorem

Remmel¹

1981

Proc. Amer. Math. Soc.

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“…Manaster and Rosenstein [1972] constructed a recursively bipartite highly recursive graph that satisfies Hall's condition for a bipartite graph to have a matching, but has no recursive matching. We discuss a natural extension of Hall's condition which assures that every such graph has a recursive matching.…”

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confidence: 99%

An Effective Version of Hall's Theorem

Kierstead¹

1983

Proceedings of the American Mathematical Society

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“…Our goal here is to find a contrast in the difficulty of finding Euler vs. Hamilton paths in a recursion theoretic setting to reflect the apparent differences in difficulty of these characterization problems. Related applications of recursion theory to combinatorial problems may be found in Jockusch [2], Manaster and Rosenstein [5], [6], and Bean [1].…”

mentioning

confidence: 99%

“…An excellent brief introduction to recursive function theory in Manaster and Rosenstein [5] will give the unfamiliar reader sufficient background to follow this work (as well as any of the above-mentioned papers).…”

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confidence: 99%

Recursive Euler and Hamilton Paths

Bean¹

1976

Proceedings of the American Mathematical Society

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Abstract. We employ recursion theoretic arguments to show that Hamilton paths for locally finite graphs are more difficult to find, in general, than Euler paths. A locally finite graph is recursive if we can effectively decide whether or not any two given vertices are adjacent, and highly recursive if we can effectively find all vertices adjacent to any given vertex. We find that there are recursive planar graphs with Euler or Hamilton paths but no such recursive paths. There are even particularly simple classes of connected, planar, highly recursive graphs for which we can show there is no effective way to decide about the existence of Euler or Hamilton paths. However, we obtain the following contrast: If a highly recursive graph has an Euler path we can effectively find a recursive Euler path; whereas, there is a planar, highly recursive graph with Hamilton paths but no recursive Hamilton path.

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Effective Matchmaking (Recursion Theoretic Aspects of a Theorem of Philip Hall)

Cited by 48 publications

References 7 publications

On the effectiveness of the Schröder-Bernstein theorem

On the effectiveness of the Schröder-Bernstein theorem

An Effective Version of Hall's Theorem

Recursive Euler and Hamilton Paths

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