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Coloring graphs without short cycles and long induced paths.

Golovach, P.A. and Paulusma, Daniel and Song, J. (2011) 'Coloring graphs without short cycles and long induced paths.', in Fundamentals of computation theory, 18th International Symposium (FCT 2011), 22-25 August 2011, Oslo, Norway ; proceedings. Berlin: Springer, pp. 193-204. Lecture notes in computer science. (6914).


The girth of a graph G is the length of a shortest cycle in G. For any fixed girth g ≥ 4 we determine a lower bound ℓ(g) such that every graph with girth at least g and with no induced path on ℓ(g) vertices is 3-colorable. In contrast, we show the existence of an integer ℓ such that testing for 4-colorability is NP-complete for graphs with girth 4 and with no induced path on ℓ vertices.

Item Type:Book chapter
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Date of first online publication:2011
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