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Applications of binary search to recursive graph theory

Author: Richard Beigel; William I Gasarch
Publisher: College Park, Md. : University of Maryland, [1987]
Series: University of Maryland at College Park.; Computer science technical report series
Edition/Format:   Book : English
Database:WorldCat
Summary:
Abstract: "We classify functions in recursive graph theory in terms of how many queries to K (or ø'' or ø''') are required to compute them. We show that (1) binary search is optimal (in terms of the number of queries to K) for finding the chromatic number of a recursive graph; no set of Turing degree less than K will suffice, (2) determining if a recursive graph has a finite chromatic number is [sigma subscript  Read more...
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Document Type: Book
All Authors / Contributors: Richard Beigel; William I Gasarch
OCLC Number: 21101611
Description: 24 p. ; 28 cm.
Series Title: University of Maryland at College Park.; Computer science technical report series
Responsibility: by Richard Beigel, William I. Gasarch.

Abstract:

Abstract: "We classify functions in recursive graph theory in terms of how many queries to K (or ø'' or ø''') are required to compute them. We show that (1) binary search is optimal (in terms of the number of queries to K) for finding the chromatic number of a recursive graph; no set of Turing degree less than K will suffice, (2) determining if a recursive graph has a finite chromatic number is [sigma subscript 2]-complete, and (3) binary search is optimal (in terms of the number of queries to ø''') for finding the recursive chromatic number of a recursive graph; no set of Turing degree less than ø''' will suffice. Some of our results have analogues in terms of asking p questions, but some do not. In particular (p + 1)-ary search is not always optimal for finding the chromatic number of a recursive graph. All results are also true for highly recursive graphs."

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