Effective coloration

Journal of Symbolic Logic 41 (2):469-480 (1976)
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Abstract

We are concerned here with recursive function theory analogs of certain problems in chromatic graph theory. The motivating question for our work is: Does there exist a recursive (countably infinite) planar graph with no recursive 4-coloring? We obtain the following results: There is a 3-colorable, recursive planar graph which, for all k, has no recursive k-coloring; every decidable graph of genus p ≥ 0 has a recursive 2(χ(p) - 1)-coloring, where χ(p) is the least number of colors which will suffice to color any graph of genus p; for every k ≥ 3 there is a k-colorable, decidable graph with no recursive k-coloring, and if k = 3 or if k = 4 and the 4-color conjecture fails the graph is planar; there are degree preserving correspondences between k-colorings of graphs and paths through special types of trees which yield information about the degrees of unsolvability of k-colorings of graphs

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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
Elements of Mathematical Logic.C. C. Chang - 1969 - Journal of Symbolic Logic 34 (1):112-112.

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