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b-Coloring graphs with large girth

✍ Scribed by Victor Campos, Victor A. E. de Farias…


Book ID
120714462
Publisher
SciELO
Year
2012
Tongue
English
Weight
259 KB
Volume
18
Category
Article
ISSN
0104-6500

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Suppose G and H are graphs. We say G is H-colorable if there is a homomorphism (edge-preserving vertex mapping) from G to H. We say a graph G is uniquely H-colorable if there is an onto homomorphism c from G to H, and any other homomorphism from G to H is the composition o o c of c with an automorph

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The odd-girth of a graph is the length of a shortest odd circuit. A conjecture by Pavol Hell about circular coloring is solved in this article by showing that there is a function f ( ) for each : 0 < < 1 such that, if the odd-girth of a planar graph G is at least f ( ), then G is (2 + )-colorable. N