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APAL
1998

On the Finiteness of the Recursive Chromatic Number

13 years 11 months ago
On the Finiteness of the Recursive Chromatic Number
A recursive graph is a graph whose vertex and edges sets are recursive. A highly recursive graph is a recursive graph that also has the following property: one can recursively determine the neighbors of a vertex. Both of these have been studied in the literature. We consider an intermediary notion: Let A be a set. An Arecursive graph is a recursive graph that also has the following property: one can recursively-in-A determine the neighbors of a vertex. We show that, if A is r.e. and not recursive, then there exists A-recursive graphs that are 2-colorable but not recursively k-colorable for any k. This is false for highly-recursive graphs but true for recursive graphs. Hence A-recursive graphs are closer in spirit to recursive graphs then to highly recursive graphs.
William I. Gasarch, Andrew C. Y. Lee
Added 21 Dec 2010
Updated 21 Dec 2010
Type Journal
Year 1998
Where APAL
Authors William I. Gasarch, Andrew C. Y. Lee
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