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## Details

Document Type: | Book |
---|---|

All Authors / Contributors: |
Richard Beigel; William I Gasarch |

OCLC Number: | 21101611 |

Description: | 24 pages ; 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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