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Some undecidable problems involving the edge-coloring and vertex-coloring of graphs

✍ Scribed by Stefan A. Burr

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
477 KB
Volume
50
Category
Article
ISSN
0012-365X

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✦ Synopsis

Certain problems involving the coloring the edges or vertices of infinite graphs are shown to be undecidable. In particular, let G and H be finite 3-connected graphs, or triangles. Then a doubly-periodic infinite graph F is constructed such that the following problem is undecidable: For a coloring of a finite subset of the edges of F red and blue, determine whether this 2-coloring can be extended to all the edges of F without either a red G or blue H occurring. In the ease of vertex-coloring, a similar result holds; here, three colors are used, and the forbidden configuration is (as usual) simply two adjacent vertices of the same color.

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